On the Efficacy of Monin–Obukhov and Bulk Richardson Surface-Layer Parameterizations over Drylands

Temple R. Lee aNOAA/Air Resources Laboratory Atmospheric Turbulence and Diffusion Division, Oak Ridge, Tennessee

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Sandip Pal bAtmospheric Science Group, Department of Geosciences, Texas Tech University, Lubbock, Texas

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Praveena Krishnan aNOAA/Air Resources Laboratory Atmospheric Turbulence and Diffusion Division, Oak Ridge, Tennessee

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Brian Hirth cNational Wind Institute, Texas Tech University, Lubbock, Texas

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Mark Heuer aNOAA/Air Resources Laboratory Atmospheric Turbulence and Diffusion Division, Oak Ridge, Tennessee
dOak Ridge Associated Universities, Oak Ridge, Tennessee

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Tilden P. Meyers aNOAA/Air Resources Laboratory Atmospheric Turbulence and Diffusion Division, Oak Ridge, Tennessee

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Rick D. Saylor aNOAA/Air Resources Laboratory Atmospheric Turbulence and Diffusion Division, Oak Ridge, Tennessee

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John Schroeder bAtmospheric Science Group, Department of Geosciences, Texas Tech University, Lubbock, Texas
cNational Wind Institute, Texas Tech University, Lubbock, Texas

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Abstract

Surface-layer parameterizations for heat, mass, momentum, and turbulence exchange are a critical component of the land surface models (LSMs) used in weather prediction and climate models. Although formulations derived from Monin–Obukhov similarity theory (MOST) have long been used, bulk Richardson (Rib) parameterizations have recently been suggested as a MOST alternative but have been evaluated over a limited number of land-cover and climate types. Examining the parameterizations’ applicability over other regions, particularly drylands that cover approximately 41% of terrestrial land surfaces, is a critical step toward implementing the parameterizations into LSMs. One year (1 January–31 December 2018) of eddy covariance measurements from a 10-m tower in southeastern Arizona and a 200-m tower in western Texas were used to determine how well the Rib parameterizations for friction velocity (u*), sensible heat flux (H), and turbulent kinetic energy (TKE) compare against MOST-derived parameterizations of these quantities. Independent of stability, wind speed regime, and season, the Rib u* and TKE parameterizations performed better than the MOST parameterizations, whereas MOST better represented H. Observations from the 200-m tower indicated that the parameterizations’ performance degraded as a function of height above ground. Overall, the Rib parameterizations revealed promising results, confirming better performance than traditional MOST relationships for kinematic (i.e., u*) and turbulence (i.e., TKE) quantities, although caution is needed when applying the Rib H parameterizations to drylands. These findings represent an important milestone for the applicability of Rib parameterizations, given the large fraction of Earth’s surface covered by drylands.

Significance Statement

Weather forecasting models rely upon complex mathematical relationships to predict temperature, wind, and moisture. Monin–Obukhov similarity theory (MOST) has long been used to forecast these quantities near the land surface, even though MOST’s limitations are well known in the scientific community. Researchers have suggested an alternative to MOST called the bulk Richardson (Rib) approach. To allow for the Rib approach to be used in weather forecasting models, the approach needs to be tested over different land-cover and climate types. In this study, we applied the Rib approach to dry areas of the United States and found that the approach better represented turbulence variables than MOST relationships. These findings are an important step toward using Rib relationships in weather forecasting models.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Temple R. Lee, temple.lee@noaa.gov

Abstract

Surface-layer parameterizations for heat, mass, momentum, and turbulence exchange are a critical component of the land surface models (LSMs) used in weather prediction and climate models. Although formulations derived from Monin–Obukhov similarity theory (MOST) have long been used, bulk Richardson (Rib) parameterizations have recently been suggested as a MOST alternative but have been evaluated over a limited number of land-cover and climate types. Examining the parameterizations’ applicability over other regions, particularly drylands that cover approximately 41% of terrestrial land surfaces, is a critical step toward implementing the parameterizations into LSMs. One year (1 January–31 December 2018) of eddy covariance measurements from a 10-m tower in southeastern Arizona and a 200-m tower in western Texas were used to determine how well the Rib parameterizations for friction velocity (u*), sensible heat flux (H), and turbulent kinetic energy (TKE) compare against MOST-derived parameterizations of these quantities. Independent of stability, wind speed regime, and season, the Rib u* and TKE parameterizations performed better than the MOST parameterizations, whereas MOST better represented H. Observations from the 200-m tower indicated that the parameterizations’ performance degraded as a function of height above ground. Overall, the Rib parameterizations revealed promising results, confirming better performance than traditional MOST relationships for kinematic (i.e., u*) and turbulence (i.e., TKE) quantities, although caution is needed when applying the Rib H parameterizations to drylands. These findings represent an important milestone for the applicability of Rib parameterizations, given the large fraction of Earth’s surface covered by drylands.

Significance Statement

Weather forecasting models rely upon complex mathematical relationships to predict temperature, wind, and moisture. Monin–Obukhov similarity theory (MOST) has long been used to forecast these quantities near the land surface, even though MOST’s limitations are well known in the scientific community. Researchers have suggested an alternative to MOST called the bulk Richardson (Rib) approach. To allow for the Rib approach to be used in weather forecasting models, the approach needs to be tested over different land-cover and climate types. In this study, we applied the Rib approach to dry areas of the United States and found that the approach better represented turbulence variables than MOST relationships. These findings are an important step toward using Rib relationships in weather forecasting models.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Temple R. Lee, temple.lee@noaa.gov

1. Introduction

Reliable near-surface temperature, moisture, and wind forecasts require that the surface-layer (SL) parameterizations schemes used within numerical weather prediction (NWP) models are able to accurately simulate exchanges of these quantities between the land surface and the overlying atmospheric boundary layer (ABL). Parameterizing these exchanges is challenging because of heterogeneity in land-cover and land-use type and the inherent complexity and nonlinearity of land–atmosphere interactions and feedbacks (e.g., Oke 1987; Stull 1988; Eltahir 1998; Pielke 2001; Dirmeyer et al. 2012; Santanello et al. 2019; Pal et al. 2020). However, the proper representation of exchanges of heat, moisture, and momentum between Earth’s surface and overlying atmosphere is essential for providing the boundary conditions for the land surface models (LSMs) used within NWP models, which is critical for obtaining reliable weather forecasts from the NWP models themselves. Furthermore, accurate SL parameterizations are required for air quality models and dispersion models to properly represent the diffusion and transport of particles, tracers, and pollutants, as well as the vertical profiles of mean horizontal wind speed within the SL (Stull 1988; Valdebenito et al. 2011; Pal and Haeffelin 2015; Pal 2016).

Decades ago, Monin–Obukhov similarity theory (MOST) was developed to represent near-surface exchange processes. MOST remains the basis for the parameterization of surface–atmosphere exchange in weather forecasting models (e.g., Best et al. 2011; Olson et al. 2021). However, MOST’s deficiencies have been known within the scientific community for decades (e.g., Businger et al. 1971; Foken 2006; Wilson 2008; Pal et al. 2013; Sun et al. 2020). MOST deficiencies arise because the original MOST formulations were derived over flat and uniform terrain (e.g., Businger et al. 1971). As we have noted in several previous studies related to this topic (e.g., Lee and Buban 2020; Lee et al. 2021; Lee and Meyers 2023), MOST issues include, for example, the assumption of a horizontally homogeneous SL (e.g., Businger et al. 1971), self-correlation (e.g., Andreas and Hicks 2002), errors in the MOST stability variable z/L (e.g., Salesky and Chamecki 2012), and poor performance in stratified SLs (e.g., Lee and Buban 2020; Sun et al. 2020), among others.

Alternative approaches to MOST have been suggested that use the Richardson number (Ri) as a scaling variable, rather than z/L (e.g., Mauritsen et al. 2007; Sorbjan 2010, 2017; Greene et al. 2022). In recent years, researchers have demonstrated that using a modified form of the Ri as a scaling variable, termed the bulk Richardson number (Rib), may be better suited than parameterizations derived from MOST for representing wind, temperature, and moisture gradients (Lee and Buban 2020); friction velocity (u*); sensible heat flux (H) and latent heat flux (E) (Lee et al. 2021); and turbulent kinetic energy (TKE) as well as temperature and water vapor mixing ratio variance (i.e., σθ and σq, respectively) (Lee and Meyers 2023) within the SL. Not only can these parameterizations be at times better than MOST, the Richardson parameterizations use bulk quantities that are arguably more straightforward to measure than quantities like u* that are included in the parameterization schemes derived from MOST.

The parameterizations that use the Rib as a scaling variable (hereinafter referred to as the Rib parameterizations) have so far been evaluated over humid subtropical climatic regimes (Lee and Buban 2020; Lee et al. 2021; Lee and Meyers 2023) using observations from three micrometeorological towers installed in northern Oklahoma during the Land–Atmosphere Feedback Experiment (LAFE; Wulfmeyer et al. 2018, 2023) and from two micrometeorological towers installed in northern Alabama during the Verification of the Origins of Rotation in Tornadoes Experiment–Southeast (VORTEX-SE; Lee et al. 2019; Wagner et al. 2019) (Fig. 1a). Evaluating the parameterizations over different land-cover types is critical for determining the parameterizations’ robustness so that they may ultimately be used in weather forecasting models in which a wide range of land-cover types are present. For example, the Rib parameterizations have not yet been evaluated over drylands. Drylands are home to more than 38% of the world’s population (Dobie 2001) and occupy approximately 41% of terrestrial land surfaces (e.g., Prăvălie 2016). Over these regions of the world, low annual precipitation leads to low soil moisture, resulting in large Bowen ratios, deep ABLs and SLs, large diurnal temperature ranges, etc. (e.g., Ma et al. 2011; Krishnan et al. 2012, 2020). These conditions are very different from the subtropical climatic regimes where the parameterizations have so far been evaluated. Given the percentage of terrestrial land surfaces occupied by drylands, it is important to evaluate the new parameterizations in these areas. Doing so is critical to move forward with the implementation of the Rib parameterizations into the next generation of operational NWP models, for example, the Rapid Refresh Forecast System (RRFS) (e.g., Benjamin et al. 2016; Dowell et al. 2022; James et al. 2022).

Fig. 1.
Fig. 1.

(a) Relative locations of the two field sites [i.e., Audubon (blue star) and RTC (green star) near Lubbock] used in this study to where previous studies have been conducted [LAFE (black star) and VORTEX-SE (red stars)] to evaluate the Rib parameterizations (i.e., Lee and Buban 2020; Lee et al. 2021; Lee and Meyers 2023). Land surface surrounding (b) Audubon (white star) and (c) RTC (white star). Images in (b) and (c) are from Google Earth.

Citation: Journal of Applied Meteorology and Climatology 62, 11; 10.1175/JAMC-D-23-0092.1

Furthermore, the previous studies that evaluated the performance of the Rib parameterizations over subtropical regimes (i.e., Lee and Buban 2020; Lee et al. 2021; Lee and Meyers 2023) only evaluated the parameterizations’ performance up to 10 m above ground level (AGL). Although the SL encompasses approximately the lowest 10% of the ABL and is where fluxes are assumed to be constant with height (e.g., Stull 1988), over drylands, the depth of the daytime ABL can exceed 3 km (e.g., Kumar et al. 2010; Ma et al. 2011; Lee and Pal 2017; Anand and Pal 2023). Because of deep ABLs over arid regions, the new parameterizations need to be tested through a larger depth of the SL than simply over the lowest 10 m. Furthermore, recent work has shown that, although parameterizations from MOST tend to agree well with observations up to about 30 m AGL, their performance degrades above this level (e.g., Sun et al. 2020). However, the newly proposed Rib parameterizations themselves have so far not been evaluated at heights above 10 m AGL.

The objectives of the present study are to 1) examine whether the Rib parameterizations outperform the MOST-derived parameterizations over drylands, 2) evaluate the Rib parameterizations beyond the SL and lower part of the ABL (up to 200 m AGL in the present study), and 3) determine any seasonal biases or limitations of the Rib parameterizations over drylands under varying weather and widely changing soil moisture regimes. To fulfill these objectives, we used 1 year of observations, obtained between 1 January 2018 and 31 December 2018, from micrometeorological towers [i.e., Audubon, which includes a 10-m tower southeast of Tucson, Arizona, and the Reese Technology Center (RTC) that includes a 200-m tower installed near Lubbock, Texas] installed in semiarid regions. We compared the results by focusing on the diurnal and seasonal performance of the MOST and Rib parameterizations at both sites. We then used observations from the 200-m tower in Texas to evaluate the parameterizations within the SL up to 200 m AGL.

2. Sites, instruments, and datasets

a. Audubon

The Audubon field site is located in southeastern Arizona about 85 km southeast of Tucson, 1473 m above mean sea level (MSL) (e.g., Krishnan et al. 2012). According to the Köppen–Geiger climate classification (e.g., Kottek et al. 2006; Peel et al. 2007), Audubon has a hot semiarid climate (i.e., climate type BSh, whereby the average temperature in the coldest month remains >0°C). The study site at Audubon (31.59°N, 110.51°W, Fig. 1b) is located on the National Audubon Society’s Appleton–Whittell Research Ranch and was established in 1969 as an ecological preserve. Observations, including turbulent fluxes, began being measured on site in June 2002 as a component of the NOAA Air Resources Laboratory Atmospheric Turbulence and Diffusion Division’s Surface Energy Budget Network (SEBN) (e.g., Krishnan et al. 2012), and the site is also a part of the AmeriFlux network (site identification: Aud; e.g., Meyers 2016). Although measurements are available from Audubon for multiple years, in the present study we focused on observations from 2018 to facilitate a comparison with observations from the tower at RTC near Lubbock, discussed in the next section.

Audubon is characterized by warm–temperate, semidesert grasslands whose height varies annually and seasonally, particularly following the onset of the North American monsoon, which typically begins in July (e.g., Carleton 1985; Stensrud et al. 1995). On-site canopy heights are typically above 40 cm, but can be as high as 70 cm. Here, we used the mean of these values and thus considered an average canopy height of 55 cm. The canopy zero-plane displacement height d and surface roughness height z0 were approximated as two-thirds and one-tenth, respectively, of the canopy height. Although we assumed a constant d and z0 for the analyses in this study, we acknowledge there is some seasonal variability in these values due to the aforementioned monsoon impacts.

Air temperature is sampled at Audubon at 1.5, 5.0, and 8.5 m AGL using platinum resistance thermometers (Thermometrics Corp. PRT, Northridge, California); humidity is sampled using a Vaisala 50Y sensor (Vaisala Oyj, Helsinki, Finland); wind speed and wind direction are sampled at 2.5, 6.0, and 9.5 m AGL using an R. M. Young 05103 anemometer (R. M. Young Co., Traverse City, Michigan); and pressure is sampled at 1.5 m AGL using a Vaisala PTB101B. These meteorological variables were sampled at intervals of 2 s using a datalogger (model CR23X; Campbell Scientific Inc., Logan, Utah) and were used to calculated 30-min means.

Measurements from a three-axis sonic anemometer (Model 81000V, R. M. Young) were sampled at 10 Hz. As noted in Krishnan et al. (2012) and briefly summarized here, we performed standard coordinate rotations. We refer the reader to, for example, Meyers (2001) and Krishnan et al. (2012) for more details on the site characteristics, meteorological measurements, and data processing. Once we computed the 30-min u*, H, and TKE, we removed physically unrealistic values, which we defined as u*<0ms1 or u*>2ms1; H < −200 W m−2 or H > 800 W m−2; and TKE < 0 m2 s−2 or TKE > 10 m2 s−2. Upon filtering physical unrealistic values, 94.1%, 93.2%, and 99.8% of the data remained for the u*, H, and TKE datasets, respectively, during the 1-yr study period.

b. RTC

RTC (33.61°N, 102.05°W) is located in northwestern Texas about 20 km west of Lubbock at 1020 m MSL (Fig. 1c). RTC has a cold semiarid climate (i.e., climate type BSk, whereby at least one month’s average temperature is <0°C) based on the Köppen–Geiger climate classification. Although there are multiple years of data available from RTC, we focused our study on measurements from 2018. In 2018, 44 cm of rainfall was recorded at RTC, which is near the long-term average for the site; 41 and 23 cm of rain fell in 2019 and 2020, respectively. Therefore, of the recent years within the data record, 2018 was most representative of the region’s climate. Furthermore, observations from 2018 were most complete, further supporting the choice to focus analyses on the measurements from 2018.

The area surrounding RTC is characterized by wild grasses, which have a long-term mean z0 of about 0.02 m, which was estimated using the same criteria as for Audubon. Because RTC is located between airport runways and grassy fields, the latter of which are frequently mowed, and is far removed from agricultural crops, we expect there to be little change in z0 and d during the study period. Therefore, we assumed that z0 and d were constants during the study period. Along the tower at RTC are a Gill R3-50 sonic anemometer, R. M. Young 43182V temperature/humidity sensor, and R. M. Young 61302V barometric pressure sensor, which are installed at each of the 10 sampling heights spaced logarithmically at 0.9, 2.4, 4.0, 10.1, 16.1, 47.3, 74.7, 116.5, 158.2, and 200 m AGL (e.g., Hamel 2022). Data are sampled at 50 Hz. We applied standard coordinate rotations and corrections to all data following the procedure described by Lee et al. (2019) prior to using the high-frequency data to calculate 30-min turbulence statistics and fluxes. As a component of our quality control and quality assurance procedures, we then removed physically unrealistic values using the same criteria as performed for the Audubon datasets. After removing physically unrealistic values from the RTC dataset, 67.7%, 82.5%, and 82.7% of the data remained for u*, H, and TKE, respectively, during the 1-yr period. We attribute the lower percentages of data availability at RTC than at Audubon to the presence of more outliers within the higher-frequency datasets at RTC that resulted in more physically unrealistic values in the 30-min fluxes and turbulence statistics.

Previous studies using RTC’s measurements found that wind turbines near the site affect wind directions between 110° and 170° for the sampling heights ≤ 4 m AGL, whereas the remaining sampling heights along the tower are affected for wind directions between 110° and 155° (Kelley and Ennis 2016). Thus, to ensure that our dataset was unaffected by highly localized impacts, we removed 30-min fluxes and turbulence statistics when the observed wind direction at any height was between 110° and 170°. Filtering data between these wind directions resulted in the removal of 11.5% of the quality-controlled data from the 2018 study period.

3. Methods

a. Evaluation of u* and H parameterizations

1) MOST parameterizations

Once the 30-min averages of u*, H, and TKE were computed from Audubon and RTC over the study period, observations from the sites were used to parameterize these quantities using the MOST and the Rib approaches. The derivation of the parameterizations for u* and H using MOST has been reported in previous studies (e.g., Jiménez et al. 2012; Lee et al. 2021) and thus is only briefly summarized here. MOST parameterizes u* as
u*=κU[ln(zdz0)ψm(zdL)+ψm(z0L)].
In Eq. (1), κ is the Von Kármán constant, U is the wind speed (m s−1), z is the measurement height (m), d is the zero-plane displacement (m), z0 is the surface roughness length (m), L is the Monin–Obukhov length scale (m), and ψm is the stability-dependent similarity function for momentum (e.g., Jiménez et al. 2012). Consequently, different functions exist for ψm depending on if L < 0 (unstable) or if L > 0 (stable). We used a value of 0.40 for κ to allow us to place our findings into the context of previous studies on this topic (e.g., Lee and Buban 2020; Lee et al. 2021; Lee and Meyers 2023), but we acknowledge that κ can range from 0.35 to 0.42 (e.g., Stull 1988).
The MOST parameterization for H is similar to the MOST u* parameterization:
H=κΔθu*ρcp[ln(z2dz1d)ψh(z2dL)+ψh(z1dL)].
In Eq. (2), Δθ is the near-surface potential temperature gradient between z1 and z2; u* is the MOST-parameterized u*; ρ is the air density; cp is the specific heat of air; z1 and z2 are the two heights at which θ is measured; and ψh is the integrated similarity function for heat (e.g., Jiménez et al. 2012). As for ψm, ψh is also stability dependent.

2) Rib parameterizations

Following Stull (1988), the Rib can be used to approximate local gradients present in the formulation for Ri as
Rib=gΔθυ¯Δzθυ¯[(Δu¯)2+(Δυ¯)2].
In Eq. (3), g is the gravitational acceleration; θυ¯ is the mean virtual potential temperature over the two heights at which temperature and wind are sampled; and u and υ are the horizontal and meridional wind components, respectively. In the present study, Rib was computed using the lowermost and uppermost sampling heights for temperature (i.e., 1.5 and 8.5 m AGL) and wind (i.e., 2.5 and 9.5 m AGL) from Audubon. When using the RTC measurements to evaluate the Rib parameterizations, Rib was computed at each height, whereby Rib at height z was computed over the range z and z − 1. Thus, Rib at 2.4 m AGL was computed using measurements from 2.4 to 0.9 m AGL, Rib at 4.0 m AGL was computed using measurements at 4.0 and 2.4 m AGL, etc.
Lee et al. (2021) parameterized u* as a function of U and the friction coefficient, Cu, that itself is a function of Rib:
u*=UCu(Rib).
In Eq. (4), the function for Cu(Rib) depends upon stability such that
Cu={λu(1ωuRib)1/3,Rib<0χuexp(γuRib),Rib>0.
In the above equations [which are modified from Eqs. (16) and (17), respectively, from Lee et al. (2021)], λu, ωu, χu, and γu are empirically derived fitting coefficients; more details on their derivation are reported in Lee et al. (2021).
Similar to how u* is parameterized as a function of Rib, H is a function of the heat transfer coefficients Ct, which is a function of Rib and the Rib-parameterized u*, that is, u*. As for Cu(Rib), Ct(Rib) also depends upon atmospheric stability:
H=Δθu*Ct(Rib)ρcp.

b. Evaluation of TKE parameterizations

TKE was computed following Eq. (7):
TKE=0.5(σu2+συ2+σw2),
where σu, συ, and σw are the standard deviations in the 30-min u, υ, and w wind components, respectively. To parameterize TKE using MOST, σu, συ, and σw were computed as a function of the MOST-parameterized u*, that is, u*, following from Lee and Meyers (2023). Thus, the parameterized σu, συ, and σw are all functions of the Obukhov length ζ, which is a stability parameter defined as ζ=(zd)/L and is used to compute σu,υ,w as
σu,υ,w=u*f(ζ).
In Eq. (8), f(ζ) is dependent upon whether ζ < 0 or ζ > 0. Thus, we compute σu,υ,w using the following equation [which is Eq. (18) from Lee and Meyers (2023)]:
σu,u,w={κU[ln(zdz0)ψm(zdL)+ψm(z0L)]ασu,υ,w(1βσu,υ,wζ)1/3,ζ<0κU[ln(zdz0)ψm(zdL)+ψm(z0L)]μσu,υ,wexp(νσu,υ,wζ),ζ>0.
In Eq. (9), ασu,υ,w, βσu,υ,w, μσu,υ,w, and νσu,υ,w are empirically derived [see Lee and Meyers (2023) for more details].
Similarly, to compute TKE using the Rib approach, σu, συ, and σw were parameterized as a function of Rib. Just like the MOST parameterizations for these quantities, these functions are also stability dependent. Thus, σu,υ,w is computed using the following equation [which is Eq. (28) in Lee and Meyers (2023)]:
σu,υ,w={Uλu,υ,w(1ωu,υ,wRib)1/3λσu,υ,w(1ωσu,υ,wRib)1/3,Rib<0Uχu,υ,wexp(γu,υ,wRib)χσu,υ,wexp(γσu,υ,wRib),Rib>0.
As in Eq. (9), in Eq. (10), λu,υ,w, ωu,υ,w, λσu,υ,w, ωσu,υ,w, χu,υ,w, γu,υ,w, χσu,υ,w, and γσu,υ,w are empirically derived; Lee and Meyers (2023) report more details on their derivation.

c. Evaluation of MOST and Rib parameterizations

The parameterized values for u*, H, and TKE were compared against the observed values for each of these quantities using the suite of observations from the two study sites. To place our results into the context of previous work on this topic (i.e., Lee et al. 2021; Lee and Meyers 2023), the mean bias error (MBE) was computed over the entire 1-yr period of interest at both sites, defined as the difference between the parameterized value and the observed value; the slope of the best-fit line between the parameterized and observed values (mb); and the coefficient of regression (R2).

The parameterizations’ performance as a function of season was also investigated. An evaluation of any seasonal variability in the parameterizations’ performance has so far not been reported in the literature, but it is important to test the parameterizations over a range of meteorological conditions that would be encountered in an operational NWP model. To this end, we evaluated the parameterizations using measurements from representative months within each season, that is, January, April, July, and October for winter, spring, summer, and fall, respectively. We acknowledge, though, that the same patterns prevail in the other months that are not shown.

Previous work has reported that the performance of the parameterizations varies as a function of wind speed (e.g., Lee et al. 2021; Lee and Meyers 2023). Thus, the performance of the MOST and the Rib parameterizations was further evaluated by distinguishing between relatively low wind speed and high wind speed regimes by computing the median wind speed at each site over the 1-yr study period. To this end, 30-min periods at Audubon were classified as having low wind speeds if the 30-min mean wind speed at 9.5 m AGL was below the median value for the time period of interest of 2.86 m s−1. If winds exceeded this value, the 30-min time period was classified into the high wind speed regime. For comparison with Audubon and with previous studies on this topic, only measurements from 10 m AGL at RTC were used for these particular analyses. At RTC, 30-min periods were classified as having low wind speeds if the 30-min mean wind speed, sampled at 10 m AGL, was below the median value for the time period of interest of 4.58 m s−1; 30-min periods with high wind speeds had wind speeds that exceeded this value.

4. Results and discussion

a. MOST and Rib parameterization performance at 10 m AGL

To compare the observations (i.e., u*, H, and TKE at 10 m AGL at both Audubon and RTC for the entire 2018 study period) with the MOST and the Rib parameterizations, the MBE, mb, and R2 between the parameterized and observed values were computed. The MBE for the parameterizations of u* for both MOST and Rib, was <0.01 m s−1 at Audubon (Fig. 2). Overall, though, the MOST parameterizations underestimated the magnitude of u*, as indicated by mb < 1, whereas the Rib parameterization had better 1:1 agreement. The magnitude of the values for u* at Audubon are comparable to previous values for u* that have been reported in the literature, as u* has been found to range from, for example, 0.2 m s−1 during the nighttime to 0.6 m s−1 during the daytime over semiarid forests (e.g., Lavi et al. 2013) and from, for example, 0.1 m s−1 during the nighttime to 0.3 m s−1 during the daytime over grasslands (e.g., Beyrich et al. 2002). Thus, the errors found between the observations of u* and the MOST and Rib parameterizations are relatively small.

Fig. 2.
Fig. 2.

Relationship between the MOST-parameterized and observed (a) u*, (b) H, and (c) TKE at Audubon at 10 m AGL in 2018. (d)–(f) As in (a)–(c), but for the Rib-parameterized values. The dotted blue line is the 1:1 line, and the solid blue line is the line of best fit. The MBE ± 1 standard deviation (σ); equation for the line of best fit, whereby Param. corresponds with the parameterized value and Obs. corresponds with the observed value; coefficient of regression (R2) and the number of samples (N) are shown in a box on each panel.

Citation: Journal of Applied Meteorology and Climatology 62, 11; 10.1175/JAMC-D-23-0092.1

Both the MOST and the Rib parameterizations overestimated the magnitude of H, with the Rib parameterizations having larger errors than the MOST parameterizations, as indicated by the MBE of 62 and 21 W m−2, respectively, and mb of 1.52 and 1.17, respectively. In contrast, the MBE was closer to 0 m2 s−2, and mb was closer to 1 in the Rib TKE parameterizations, but there was significantly more scatter, as indicated by the lower R2 values for the Rib TKE parameterizations as compared with the MOST TKE parameterizations. These results were consistent when distinguishing between unstable regimes (i.e., when ζ < 0 or Rib < 0) and stable regimes (i.e., when ζ > 0 or Rib > 0), as well as when comparing the daily mean observed u*, H, and TKE with the MOST- and Rib-parameterized u*, H, and TKE (not shown).

At 10 m AGL at RTC for the 1-yr study period, the MOST and Rib parameterizations generally underestimated u*, but mb was closer to 1 for the Rib parameterizations (i.e., mb = 0.88) than it was for the MOST parameterizations (i.e., mb = 0.70) (Fig. 3). Unlike at Audubon, both parameterizations underestimated the magnitude of H, but the parameterizations performed similarly with respect to mb. Furthermore, both the MOST and the Rib parameterizations underestimated TKE, but mb was notably larger for the Rib parameterizations (i.e., mb = 0.84) than for the MOST parameterizations (i.e., mb = 0.52). Also notable was that there was considerably more scatter at RTC than at Audubon, as R2 was lower for both sets of parameterizations for all variables considered. Consistent with our findings from Audubon, our results did not show significant dependence on SL stability (not shown).

Fig. 3.
Fig. 3.

As in Fig. 2, but for RTC.

Citation: Journal of Applied Meteorology and Climatology 62, 11; 10.1175/JAMC-D-23-0092.1

b. Evaluation of time-of-day dependency

When distinguishing by time of day, over the entire 1-yr period of interest at both sites, the Rib parameterizations tended to overestimate daytime values of u*, H, and TKE both at Audubon and at RTC, as evident from the mean diurnal cycles of the observed and parameterized u*, H, and TKE at 10 m AGL (Fig. 4). The overestimates at this sampling height were larger at RTC than at Audubon, as the Rib approach overestimated u* by around 0.05 m s−1 during the nighttime and by about 0.10 m s−1 during the daytime. In contrast, there was excellent agreement between the observed and Rib-parameterized u* at Audubon throughout the mean diurnal cycle, whereas the MOST-parameterized u* was ∼0.05 m s−1 larger than the observed values during the nighttime. Although both the MOST and the Rib parameterizations overestimated H at Audubon, MOST had better agreement with the observations, which is a point we discuss in more detail in the next section. In contrast, the MOST parameterizations underestimated the mean TKE at both sites, with the largest underestimates during the daytime at RTC, when TKE was underestimated by around 1 m2 s−2.

Fig. 4.
Fig. 4.

Mean diurnal cycle of (a) u*, (b) H, and (c) TKE at Audubon at 10 m AGL in 2018. (d)–(f) As in (a)–(c), but for 10 m AGL at RTC. Black, red, and blue lines show the observed values, MOST-parameterized values, and Rib-parameterized values, respectively.

Citation: Journal of Applied Meteorology and Climatology 62, 11; 10.1175/JAMC-D-23-0092.1

c. Evaluation of seasonal dependency

Discussion so far has focused on the performance of the MOST and Rib parameterizations irrespective of time of year. An investigation specifically distinguishing the parameterizations’ performance as a function of season has so far not been reported in the literature but is important for capturing a range of meteorological conditions at both sites over a climatologically representative year (cf. section 2). To this end, the MBE, mb, and R2 for the u*, H, and TKE MOST and Rib parameterizations were compared in each of the representative months within each season at Audubon and RTC.

The MBEs between the parameterized and observed u* were comparable for both MOST and Rib parameterizations at both sites in all seasons (Fig. 5a), and the same was true for the standard deviations in the MBEs (Fig. 5b). In contrast, mb was closer to 1 in all seasons at both sites for the Rib parameterizations than for the MOST parameterizations (Fig. 5c). At Audubon, R2 was closer to 1 for the Rib u* parameterizations during the winter, spring, and fall, but the opposite was true in the summer (Fig. 5d). At RTC, R2 was slightly larger for the Rib u* parameterizations than for the MOST u* parameterizations during the winter and summer but slightly lower during the fall.

Fig. 5.
Fig. 5.

(a) MBE, (b) σ, (c) mb, and (d) R2 between the parameterized and observed u*, H, and TKE for the MOST parameterizations at Audubon (red circle), Rib parameterizations at Audubon (blue circle), MOST parameterizations at RTC (red star), and Rib parameterizations at RTC (blue star) in January, April, July, and October 2018. In (a) and (b), the MBEs and σ values for H have been multiplied by 0.01 W m−2 to show all MBEs and σ values on the same graphs; for u* and TKE, the MBEs and the σ values shown have units of m s−1 and m2 s−2, respectively. There is a horizontal black line in (a) where MBE = 0 and in (c) where mb = 1. Vertical black lines are used to separate among the seasonal performance of the MOST and Rib parameterizations for u*, H, and TKE.

Citation: Journal of Applied Meteorology and Climatology 62, 11; 10.1175/JAMC-D-23-0092.1

When evaluating the H parameterizations over the different seasons at both sites, we found the MBEs were closer to 0 W m−2 for the MOST parameterizations than for the Rib parameterizations (Fig. 5a), and the standard deviations in these differences were generally larger for the Rib parameterizations than for the MOST parameterizations (Fig. 5b). Furthermore, mb was closer to 1 in all seasons at both sites, except for during the fall at RTC (Fig. 5c). The R2 was larger for the MOST parameterizations than for the Rib parameterizations for all seasons at Audubon and also during the winter and spring at RTC (Fig. 5d).

In contrast to the performance of the H parameterizations, the Rib TKE parameterizations generally had MBEs closer to 0 m2 s−2 (Fig. 5a) and values of mb closer to 1 than the MOST parameterizations across all seasons at both Audubon and RTC (Fig. 5c). However, there was considerably more scatter present for the Rib TKE parameterizations than for the MOST parameterizations, as evident by the larger standard deviation in the mean values (Fig. 5b) and the lower values of R2 for the Rib parameterizations (Fig. 5d).

When distinguishing by time of day within each of the different seasons, we found that, irrespective of season, the MOST parameterizations generally overestimated the nighttime u* but underestimated the daytime u* (Fig. 6). In contrast to the performance of the MOST parameterizations, the Rib parameterizations generally agreed quite well but did overestimate daytime u* by about 0.05 m s−1 in April. However, we acknowledge there was considerable variability around these values, as indicated by standard deviations of ∼0.15–0.20 m s−1 during the daytime, both in the observed u* as well as in u* derived from the MOST and Rib parameterizations.

Fig. 6.
Fig. 6.

Mean diurnal cycle of u* in (a) January 2018, (b) April 2018, (c) July 2018, and (d) October 2018 at 10 m AGL at Audubon. Black, red, and blue lines show the observed values, MOST-parameterized values, and Rib-parameterized values, respectively.

Citation: Journal of Applied Meteorology and Climatology 62, 11; 10.1175/JAMC-D-23-0092.1

There was more spread in the performance of the parameterizations at RTC in the different seasons. The Rib parameterizations overestimated u* by up to 0.1 m s−1 in July (Fig. 7), whereas the MOST parameterizations tended to underestimate the magnitude of u* by as much as the 0.15 m s−1 in the mid–late morning in October. Overall, though, the performance of the different parameterizations of u* did not show significant differences as a function of season at Audubon.

Fig. 7.
Fig. 7.

As in Fig. 6, but for RTC. Note the same y axis as in Fig. 6 was used to facilitate a comparison between the sites and across seasons.

Citation: Journal of Applied Meteorology and Climatology 62, 11; 10.1175/JAMC-D-23-0092.1

When evaluating the performance of the MOST and Rib parameterizations for the H mean diurnal cycle as a function of season (Fig. 8), we found that the MOST parameterizations generally performed better than the Rib parameterizations at Audubon. Although the MOST parameterizations overestimated daytime H in all seasons except for summer, the overestimates from MOST were smaller than for the Rib parameterizations. The largest H overestimate by the MOST parameterizations was ∼80 W m−2 in January, whereas daytime differences were generally <50 W m−2 during the remaining seasons.

In contrast to the performance of the MOST H parameterizations, the Rib H parameterizations overestimated daytime H by nearly 200 W m−2 in January and April and by up to 150 W m−2 in July and October (Fig. 8). The large overestimates of H are suspected to be caused by the very dry conditions at this site, which are investigated in more detail using ancillary measurements from Audubon. Throughout much of the year, 5-cm soil moisture is generally <0.1 m3 m−3, and the mean maximum daytime values for the latent heat fluxes are <100 W m−2. Soil moisture increases following the onset of precipitation during the North American monsoon in July (e.g., Krishnan et al. 2012), resulting in latent heat fluxes > 150 W m−2 during the late summer (not shown). Consequently, mean values of the Bowen ratio, β, (i.e., the ratio of the sensible heat flux to the latent heat flux) at the site were around 2 during the afternoon (1200–1600 LST) in the summer months, but were double this value during the afternoon in the spring and fall. Furthermore, near-surface potential temperature gradients are largest premonsoon. Since the Rib H parameterizations are a function of the potential temperature difference between two sampling heights [cf. Eq. (6)], we suspect these large differences in near-surface temperature may contribute to the large premonsoon H overestimates by the Rib parameterizations. Although previous work evaluating the Rib H parameterizations generally found good agreement with the observations over subtropical regions (i.e., Lee et al. 2021), at those locations the Rib parameterizations also tended to overestimate H when H was large, which is a finding consistent with our findings at Audubon.

Fig. 8.
Fig. 8.

Mean diurnal cycle of H in (a) January 2018, (b) April 2018, (c) July 2018, and (d) October 2018 at Audubon. Black, red, and blue lines show the observed values, MOST-parameterized values, and Rib-parameterized values, respectively.

Citation: Journal of Applied Meteorology and Climatology 62, 11; 10.1175/JAMC-D-23-0092.1

As was the case for u*, results were mixed with respect to the performance of the parameterizations for H at RTC. In January and October, both the MOST and the Rib parameterizations well simulated the mean diurnal cycle of H (Fig. 9). Unlike at Audubon, in April and July, both sets of parameterizations underestimated H, although the MOST parameterizations showed slightly better agreement with observations than the Rib parameterizations during these time periods. Consistent with Audubon, though, the absolute value of the differences among the parameterizations was generally larger during April and July than January and October. We speculate that the better agreement for the MOST H parameterizations as compared with the Rib H parameterizations arises because the Rib parameterizations were developed in a less arid region (i.e., a more subtropical climatic regime) than the Audubon and RTC sites. At Audubon and RTC, H represents a larger component of the surface energy balance. The poorer performance of the Rib H parameterizations as compared with the traditional MOST parameterizations for H indicates that caution is warranted when applying the Rib H parameterizations to drylands.

Fig. 9.
Fig. 9.

As in Fig. 8, but for RTC. Note the same y axis as in Fig. 8 was used to facilitate a comparison between the sites and across seasons.

Citation: Journal of Applied Meteorology and Climatology 62, 11; 10.1175/JAMC-D-23-0092.1

Despite the performance of the Rib H parameterizations, the Rib TKE parameterizations generally performed better than the MOST TKE parameterizations in the different seasons at Audubon in all seasons except for winter, when the Rib parameterizations overestimated TKE by up to 0.5 m2 s−2 during the late morning. In contrast, the MOST parameterizations well simulated the magnitude of the mean diurnal cycle at the site during this time period (Fig. 10). During the other seasons, the Rib parameterizations well captured the magnitude of the mean diurnal cycle, but the maximum occurred 2 h earlier in July because the Rib parameterization overestimated the magnitude of συ around this time (not shown). At RTC, the Rib TKE parameterizations performed better than the MOST parameterizations in January, April, and July but significantly overestimated TKE in October, with parameterized values at times up to 1.5 m2 s−2 larger than the observations during the daytime (Fig. 11), which we attribute to the parameterizations overestimating συ and σw.

Fig. 10.
Fig. 10.

Mean diurnal cycle of TKE in (a) January 2018, (b) April 2018, (c) July 2018, and (d) October 2018 at 10 m AGL at Audubon. Black, red, and blue lines show the observed values, MOST-parameterized values, and Rib-parameterized values, respectively.

Citation: Journal of Applied Meteorology and Climatology 62, 11; 10.1175/JAMC-D-23-0092.1

Fig. 11.
Fig. 11.

As in Fig. 10, but for RTC. Note the same y axis as in Fig. 10 was used to facilitate a comparison between the sites and across seasons.

Citation: Journal of Applied Meteorology and Climatology 62, 11; 10.1175/JAMC-D-23-0092.1

d. Evaluation of wind speed dependency

As noted in section 3c, previous studies have reported that the performances of the MOST and Rib parameterizations exhibit differences between subsets of cases when wind speeds are low compared with the subset of cases when wind speeds are comparatively high (i.e., Lee et al. 2021; Lee and Meyers 2023). When distinguishing between 30-min periods at Audubon with low winds (i.e., defined as wind speeds below the median value for the period of 2.86 m s−1) compared with those periods with comparatively high wind speeds (i.e., wind speeds > 2.86 m s−1), the Rib u* and TKE parameterizations generally performed better than the MOST parameterizations both for the subset of cases with comparatively low wind speeds at the site (Figs. 12a–f) and for the subset of cases with comparatively high wind speeds at the site (Figs. 12g–l), as indicated by mb nearer to 1. The opposite was true for H, as the Rib parameterization had larger mb and MBE and either comparable or lower R2 than the MOST parameterizations.

Fig. 12.
Fig. 12.

Relationship between the MOST-parameterized and observed (a) u*, (b) H, and (c) TKE at Audubon at 10 m AGL in 2018 for low wind speeds (i.e., identified as 30-min periods with mean wind speeds < 2.86 m s−1). (d)–(f) As in (a)–(c), but for the Rib-parameterized values. Relationship between the MOST-parameterized and observed (g) u*, (h) H, and (i) TKE at Audubon at 10 m AGL in 2018 for 30-min periods with high wind speeds (i.e., identified as 30-min periods with mean wind speeds > 2.86 m s−1). (j)–(l) As in (g)–(i), but for the Rib-parameterized values. The MBE ± 1σ; equation for the line of best fit, whereby Param. corresponds with the parameterized value and Obs. corresponds with the observed value; R2 and N are shown in a box on each panel.

Citation: Journal of Applied Meteorology and Climatology 62, 11; 10.1175/JAMC-D-23-0092.1

Consistent results were seen at 10 m AGL at RTC (Fig. 13) when distinguishing between low wind speed and high wind speed regimes. Higher median wind speeds were observed at RTC than at Audubon (4.58 m s−1 at 10 m AGL at RTC vs 2.86 m s−1 at Audubon) due to the comparatively flat terrain surrounding RTC and routine presence of downslope winds off the Mexican plateau to the west. At RTC, in the subset of 30-min periods with wind speeds less than the median value of 4.58 m s−1 over the time period of interest, mb for the MOST u* parameterizations was 0.31 but was 0.52 for the Rib parameterizations. Similarly, for the subset of conditions with high wind speeds (i.e., 30-min periods in which the wind speed was greater than the median value of 4.58 m s−1), mb values for the MOST and Rib parameterizations were 0.57 and 0.73, respectively. Similar improvements in the TKE parameterizations were found under low wind speed and high wind speed conditions. Under low wind speeds, mb values for the MOST and Rib parameterizations were 0.17 and 0.35, respectively, whereas for high wind speeds mb was 0.51 for the MOST and 0.80 for the Rib parameterizations. In contrast, mb was lower for the Rib H parameterizations than for the MOST parameterizations in both subsets of cases, decreasing from 0.70 to 0.62 in the subset of cases with low wind speeds and from 0.82 to 0.79 in the subset of cases with high wind speeds.

Fig. 13.
Fig. 13.

Relationship between the MOST-parameterized and observed (a) u*, (b) H, and (c) TKE at RTC at 10 m AGL in 2018 for low wind speeds (i.e., identified as 30-min periods with wind speeds < 4.58 m s−1). (d)–(f) As in (a)–(c), but for the Rib-parameterized values. Relationship between the MOST-parameterized and observed (g) u*, (h) H, and (i) TKE at RTC at 10 m AGL in 2018 for 30-min periods with high wind speeds (i.e., identified as 30-min periods with wind speeds > 4.58 m s−1). (j)–(l) As in (g)–(i), but for the Rib-parameterized values. The dotted blue line is the 1:1 line and the solid blue line is the line of best fit. The MBE ± 1σ; equation for the line of best fit, whereby Param. corresponds with the parameterized value and Obs. corresponds with the observed value; R2 and N are shown in a box on each panel.

Citation: Journal of Applied Meteorology and Climatology 62, 11; 10.1175/JAMC-D-23-0092.1

The findings from both Audubon and RTC are in contrast to previous studies that have evaluated the performance of the MOST and Rib parameterizations as a function of wind speed (i.e., Lee et al. 2021; Lee and Meyers 2023). Lee et al. (2021) reported that the Rib H parameterizations performed considerably better than the MOST H parameterizations across multiple sites in subtropical climates under weak mean wind speeds, but their work found less consistent performance for the u* parameterizations. Similarly, Lee and Meyers (2023) reported that the Rib TKE parameterizations performed better than the MOST TKE parameterizations under weak mean wind speeds.

e. Parameterization performance as a function of height

Discussion so far has focused on how well the MOST and Rib parameterizations perform at 10 m AGL, which is the sampling height at which the Rib parameterizations were developed and have so far been evaluated in previous studies (e.g., Lee and Buban 2020; Lee et al. 2021; Lee and Meyers 2023). Evaluating how well the MOST and Rib parameterizations simulate u*, H, and TKE is of particular importance over arid and semiarid regions, where the daytime ABL can exceed 3 km in depth (e.g., Kumar et al. 2010; Ma et al. 2011; Lee and Pal 2017) and thus the SL can be several hundred meters deep (e.g., Hamel 2022). To this end, the RTC tower observations were used to determine how well the MOST and Rib parameterizations performed at heights above 10 m AGL. To quantify the performance of the parameterizations as a function of height, the observed u*, H, and TKE at each of the heights were compared against the MOST- and Rib-parameterized values at each height by computing the MBE between the parameterized and observed values, as well as the mb and R2. This analysis was performed for the entire 1-yr period of interest, as well as for afternoon [which we defined as between 1200 and 1600 LST (LST = UTC − 6)] and nighttime (which we defined as between 0000 and 0400 LST) when fluxes are typically at their maximum and minimum values, respectively.

When considering all times of the day and all seasons, the performance of the MOST and Rib parameterizations for u* degraded as a function of height, as evident by the increase in MBE and decrease in both mb and R2 (Figs. 14a–c). The most significant deviations in the parameterization performance occurred above 50 m AGL. The MBE was smaller for the MOST parameterizations than for the Rib parameterizations, which may be due to the larger amounts of scatter as indicated by the lower values for R2. However, mb was closer to 1 for all heights for the Rib parameterizations than for the MOST parameterizations.

Fig. 14.
Fig. 14.

(a) MBE, (b) mb, and (c) R2 between the parameterized and observed u* for all times of the day at RTC. (d)–(f) As in (a)–(c), but only for 1200–1600 LST. (g)–(i) As in (a)–(c), but only for 0000–0400 LST. Red lines show results from the MOST parameterizations, and blue lines show results from the Rib parameterizations. Note that the y axes have logarithmic scales in all panels. There is a vertical black line in (a), (d), and (g) where MBE = 0 and in (b), (e), and (h) where mb = 1.

Citation: Journal of Applied Meteorology and Climatology 62, 11; 10.1175/JAMC-D-23-0092.1

Results for the entire day were consistent with results when distinguishing by time of day. Although the MBEs were larger during the afternoon because of the larger magnitude of u*, both the MOST and the Rib parameterizations performed better during the afternoon than nighttime, as shown by mb being closer to 1 during the afternoon than during nighttime and also by the larger values for R2 during the afternoon than nighttime (Figs. 14d–i).

The MOST and Rib H parameterizations performed similarly as a function of height, irrespective of time of day (Fig. 15). As was the case for u*, the MBEs for the H parameterizations were larger during the afternoon than nighttime simply due to the much larger magnitude of the afternoon heat fluxes as compared with the nighttime values, which are typically around 0 W m−2. Consistent with what was found in the mean diurnal cycles at 10 m AGL (cf. sections 4c and 4d), there was a mean negative bias at this level that was present for the majority of the heights. The value of mb was generally around 0.5 below 100 m AGL but, along with R2, markedly decreased above this height, indicating a reduction in the performance of the parameterizations here.

Fig. 15.
Fig. 15.

As in Fig. 14, but for H.

Citation: Journal of Applied Meteorology and Climatology 62, 11; 10.1175/JAMC-D-23-0092.1

Unlike the parameterizations for H, there were significant differences in how well the MOST and Rib TKE parameterizations performed as a function of height (Fig. 16). When all times of day were considered, the MBEs were consistently smaller for the Rib parameterizations than for the MOST parameterizations up to about 50 m AGL. Irrespective of time of day, the magnitude of the MBEs increased as a function of height, indicating a reduction in the parameterizations’ performance with height in the SL. The values for mb were overall larger for the Rib parameterizations than for the MOST parameterizations and were closer to 1. The exception was the measurements from 47 to 74 m AGL during the afternoon, where the Rib parameterizations overestimated TKE by on average 2 m2 s−2, and mb was ∼2.

Fig. 16.
Fig. 16.

As in Fig. 14, but for TKE.

Citation: Journal of Applied Meteorology and Climatology 62, 11; 10.1175/JAMC-D-23-0092.1

Unlike for the u* and H parameterizations, significant differences in the performance of the MOST and Rib TKE parameterizations were found between the afternoon and nighttime. In the lowest few tens of meters, R2 was between 0.6 and 0.8 for both the MOST and the Rib parameterizations during the afternoon, but markedly decreased above this height to <0.2 above 100 m AGL. In contrast, nighttime values for R2 were below 0.2 for all sampling heights above 50 m AGL.

Although no studies have yet evaluated the Rib parameterizations as a function of height above the land surface, in particular above the SL, previous studies evaluating MOST parameterizations have reported similar findings as reported here for u*, H, and TKE. For example, Sun et al. (2020) found that the parameterizations performed well in the lowest ∼30 m of the SL, but that errors increased above this height. The fact that the performance of both the MOST and the Rib parameterizations generally degrades as a function of height should not be too troubling, though, when using the parameterizations in NWP modeling applications because the SL oftentimes only extends up to the model’s first prognostic level, which is typically in the lowest couple tens of meters (e.g., McTaggart‐Cowan et al. 2019; Olson et al. 2021).

5. Summary, conclusions, and outlook

Ri-based parameterizations have recently been suggested as an alternative to traditional parameterizations derived from MOST (e.g., Mauritsen et al. 2007; Sorbjan 2010, 2017; Lee and Buban 2020; Lee et al. 2021; Greene et al. 2022; Lee and Meyers 2023). In the present study, 1 year of observations from two semiarid sites, one located in southeastern Arizona and a second located in northwestern Texas, were used to determine how well recently suggested Rib parameterizations for u*, H, and TKE performed against MOST-derived parameterizations of these quantities. The MOST and Rib parameterizations were evaluated by comparing the parameterized values against the observed values from both sites by computing the MBE, mb, and R2. Based on the MBE and mb for the entire study period, which are summarized in Table 1, the Rib parameterizations for u* and TKE overall performed better than the MOST parameterizations, whereas the MOST parameterizations better represented H than the Rib parameterizations. These results were consistent across different stability regimes, seasons, and wind speed regimes.

Table 1.

MBE, mb, and R2 between the parameterized and observed u*, H, and TKE for the MOST parameterizations at Audubon, Rib parameterizations at Audubon, MOST parameterizations at RTC, and Rib parameterizations at RTC over the 2018 study period. The MBE values for u*, H and TKE have units of m s−1, W m−2, and m2 s−2, respectively.

Table 1.

Observations from a 200-m tower in northwestern Texas were also used to evaluate how well the parameterizations performed as a function of height, and similar conclusions were found regarding the performance of the Rib parameterizations compared with the MOST parameterizations. As expected, and consistent with previous work with MOST (e.g., Sun et al. 2020), the performance of the parameterizations degraded as a function of height above ground level, with the largest decreases occurring above about 50 m. Nevertheless, the results in the present study are valuable for demonstrating the applicability of the Rib parameterizations for the lowest part of the ABL over semiarid and arid regions.

As has been reported in previous studies and therefore only briefly summarized here (e.g., Lee and Buban 2020; Lee et al. 2021; Lee and Meyers 2023), both the MOST and the Rib parameterizations have statistical self-correlation, which has been well documented for MOST (e.g., Hicks 1978, 1981). However, the Rib parameterizations rely on bulk quantities (e.g., Lee et al. 2021; Lee and Meyers 2023). Furthermore, ζ in MOST is a function of u*3, and thus errors in measured u* become more significant because u* is cubed, which can induce errors in ζ (e.g., Markowski et al. 2019; Lee et al. 2021) and the subsequent computation of the fluxes using MOST (e.g., Lee et al. 2021). A downside of the Rib parameterizations as compared with parametrizations derived from MOST, though, is that the Rib parameterizations do not directly consider surface roughness and canopy height. These terms are explicitly quantified through the z0 and d terms [cf. Eqs. (1) and (2)] in MOST. Despite the strengths and weaknesses of the MOST and Rib parameterizations discussed here, the findings in the present study suggest that, whereas caution is necessary when using the Rib H parameterizations in drylands, the Rib parameterizations generally outperform MOST for kinematic (i.e., u*) and turbulence (i.e., TKE) quantities. Because drylands cover approximately 41% of terrestrial land surfaces, the findings in this study represent an important milestone for the application of newly developed SL parameterizations for potential use in NWP models.

Future work should use the multiyear datasets from both Audubon and RTC to investigate the performance of these parameterizations across multiple years to encompass an even broader range of meteorological conditions at both sites (i.e., very dry years and very wet years). The inclusion of datasets from other long-term micrometeorological towers located in other climate regimes and land-cover types with different surface roughness and canopy heights, as well as using observations derived from other platforms (e.g., small uncrewed aircraft systems) used routinely to sample the SL, will permit further evaluation of, and allow for potential modifications to, the new SL parameterizations. Future work may also consider the inclusion of the seasonal variability in surface roughness and/or canopy height in the Rib parameterizations, or may also explicitly consider SL moisture through, for example, the inclusion of the Bowen ratio within the parameterizations. These analyses, coupled with testing the newly suggested Rib parameterizations in large eddy simulations, will be another critical next step toward ultimately implementing the SL parameterizations into the next generation of NWP models.

Acknowledgments.

Coauthor SP was supported by a Texas Tech University faculty startup grant, and this work was an integrated component of the Land-Atmosphere Interactions during Morning and Evening Transitions (LAI-MET) research initiative lead by coauthor SP at Texas Tech University. Furthermore, we thank staff members and engineers at Texas Tech University’s National Wind Institute for routine monitoring and maintenance of the micrometeorological measurements at the 10 levels of the 200-m tower at RTC. We also thank the three anonymous reviewers for their valuable feedback, which allowed for us to clarify several points in the manuscript. Finally, we note that the results and conclusions of this study, as well as any views expressed herein, are those of the authors and do not necessarily reflect the views of NOAA or the Department of Commerce.

Data availability statement.

The datasets from Audubon, as well as the high-frequency turbulence measurements used to generate the 30-min fluxes and turbulence statistics from the 200-m tower at the Reese Technology Center, are available upon request from the corresponding author.

REFERENCES

  • Anand, M., and S. Pal, 2023: Exploring atmospheric boundary layer depth variability in frontal environments over an arid region. Bound.-Layer Meteor., 186, 251285, https://doi.org/10.1007/s10546-022-00756-z.

    • Search Google Scholar
    • Export Citation
  • Andreas, E. L., and B. B. Hicks, 2002: Comments on “Critical test of the validity of Monin–Obukhov similarity during convective conditions”. J. Atmos. Sci., 59, 26052607, https://doi.org/10.1175/1520-0469(2002)059<2605:COCTOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Benjamin, S. G., and Coauthors, 2016: A North American hourly assimilation and model forecast cycle: The Rapid Refresh. Mon. Wea. Rev., 144, 16691694, https://doi.org/10.1175/MWR-D-15-0242.1.

    • Search Google Scholar
    • Export Citation
  • Best, M. J., and Coauthors, 2011: The Joint UK Land Environment Simulator (JULES), model description—Part 1: Energy and water fluxes. Geosci. Model Dev., 4, 677699, https://doi.org/10.5194/gmd-4-677-2011.

    • Search Google Scholar
    • Export Citation
  • Beyrich, F., and Coauthors, 2002: Experimental determination of turbulent fluxes over the heterogeneous LITFASS area: Selected results from the LITFASS-98 experiment. Theor. Appl. Climatol., 73, 1934, https://doi.org/10.1007/s00704-002-0691-7.

    • Search Google Scholar
    • Export Citation
  • Businger, J. A., J. C. Wyngaard, Y. Izumi, and E. F. Bradley, 1971: Flux-profile relationships in the atmospheric surface layer. J. Atmos. Sci., 28, 181189, https://doi.org/10.1175/1520-0469(1971)028<0181:FPRITA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Carleton, A. M., 1985: Synoptic and satellite aspects of the southwestern U.S. summer ‘monsoon’. J. Climatol., 5, 389402, https://doi.org/10.1002/joc.3370050406.

    • Search Google Scholar
    • Export Citation
  • Dirmeyer, P. A., and Coauthors, 2012: Evidence for enhanced land–atmosphere feedback in a warming climate. J. Hydrometeor., 13, 981995, https://doi.org/10.1175/JHM-D-11-0104.1.

    • Search Google Scholar
    • Export Citation
  • Dowell, D. C., and Coauthors, 2022: The High-Resolution Rapid Refresh (HRRR): An hourly updating convection-allowing forecast model. Part I: Motivation and system description. Wea. Forecasting, 37, 13711395, https://doi.org/10.1175/WAF-D-21-0151.1.

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  • Eltahir, E. A. B., 1998: A soil moisture–rainfall feedback mechanism: 1. Theory and observations. Water Resour. Res., 34, 765776, https://doi.org/10.1029/97WR03499.

    • Search Google Scholar
    • Export Citation
  • Foken, T., 2006: 50 years of the Monin–Obukhov similarity theory. Bound.-Layer Meteor., 119, 431447, https://doi.org/10.1007/s10546-006-9048-6.

    • Search Google Scholar
    • Export Citation
  • Greene, B. R., S. T. Kral, P. B. Chilson, and J. Reuder, 2022: Gradient-based turbulence estimates from multicopter profiles in the Arctic stable boundary layer. Bound.-Layer Meteor., 183, 321353, https://doi.org/10.1007/s10546-022-00693-x.

    • Search Google Scholar
    • Export Citation
  • Hamel, M., 2022: Convective boundary layer turbulence profiling over an arid region using a 200m tall-tower and Doppler lidar measurements. M.S. thesis, Dept. of Geosciences, Texas Tech University, 143 pp., https://ttu-ir.tdl.org/bitstreams/f52ba1b4-95e1-42cd-b3d3-4f1d2bd7c8fc/download.

  • Hicks, B. B., 1978: Some limitations of dimensional analysis and power laws. Bound.-Layer Meteor., 14, 567569, https://doi.org/10.1007/BF00121895.

    • Search Google Scholar
    • Export Citation
  • Hicks, B. B., 1981: An examination of turbulence statistics in the surface boundary layer. Bound.-Layer Meteor., 21, 389402, https://doi.org/10.1007/BF00119281.

    • Search Google Scholar
    • Export Citation
  • James, E. P., and Coauthors, 2022: The High-Resolution Rapid Refresh (HRRR): An hourly updating convection-allowing forecast model. Part II: Forecast performance. Wea. Forecasting, 37, 13971417, https://doi.org/10.1175/WAF-D-21-0130.1.

    • Search Google Scholar
    • Export Citation
  • Jiménez, P. A., J. Dudhia, J. F. González-Rouco, J. Navarro, J. P. Montávez, and E. García-Bustamante, 2012: A revised scheme for the WRF surface layer formulation. Mon. Wea. Rev., 140, 898918, https://doi.org/10.1175/MWR-D-11-00056.1.

    • Search Google Scholar
    • Export Citation
  • Kelley, C. L., and B. L. Ennis, 2016: SWiFT site atmospheric characterization. SANDIA Tech. Rep. SAND-2016-0216, 82 pp., https://www.osti.gov/servlets/purl/1237403.

  • Kottek, M., J. Grieser, C. Beck, B. Rudolf, and F. Rubel, 2006: World map of the Köppen-Geiger climate classification updated. Meteor. Z., 15, 259263, https://doi.org/10.1127/0941-2948/2006/0130.

    • Search Google Scholar
    • Export Citation
  • Krishnan, P., T. P. Meyers, R. L. Scott, L. Kennedy, and M. Heuer, 2012: Energy exchange and evapotranspiration over two temperate semi-arid grasslands in North America. Agric. For. Meteor., 153, 3144, https://doi.org/10.1016/j.agrformet.2011.09.017.

    • Search Google Scholar
    • Export Citation
  • Krishnan, P., T. P. Meyers, S. J. Hook, M. Heuer, D. Senn, and E. J. Dumas, 2020: Intercomparison of in situ sensors for ground-based land surface temperature measurements. Sensors, 20, 5268, https://doi.org/10.3390/s20185268.

    • Search Google Scholar
    • Export Citation
  • Kumar, M., C. Mallik, A. Kumar, N. C. Mahanti, and A. M. Shekh, 2010: Evaluation of the boundary layer depth in semi-arid region of India. Dyn. Atmos. Oceans, 49, 96107, https://doi.org/10.1016/j.dynatmoce.2009.01.002.

    • Search Google Scholar
    • Export Citation
  • Lavi, A., D. K. Farmer, E. Segre, T. Moise, E. Rotenberg, J. L. Jimenez, and Y. Rudich, 2013: Fluxes of fine particles over a semi-arid pine forest: Possible effects of a complex terrain. Aerosol Sci. Technol., 47, 906915, https://doi.org/10.1080/02786826.2013.800940.

    • Search Google Scholar
    • Export Citation
  • Lee, T. R., and S. Pal, 2017: On the potential of 25 years (1991–2015) of rawinsonde measurements for elucidating climatological and spatiotemporal patterns of afternoon boundary layer depths over the contiguous US. Adv. Meteor., 2017, 6841239, https://doi.org/10.1155/2017/6841239.

    • Search Google Scholar
    • Export Citation
  • Lee, T. R., and M. Buban, 2020: Evaluation of Monin–Obukhov and bulk Richardson parameterizations for surface–atmosphere exchange. J. Appl. Meteor. Climatol., 59, 10911107, https://doi.org/10.1175/JAMC-D-19-0057.1.

    • Search Google Scholar
    • Export Citation
  • Lee, T. R., and T. P. Meyers, 2023: New parameterizations of turbulence statistics for the atmospheric surface layer. Mon. Wea. Rev., 151, 85103, https://doi.org/10.1175/MWR-D-22-0071.1.

    • Search Google Scholar
    • Export Citation
  • Lee, T. R., M. Buban, D. D. Turner, T. P. Meyers, and C. B. Baker, 2019: Evaluation of the High-Resolution Rapid Refresh (HRRR) model using near-surface meteorological and flux observations from northern Alabama. Wea. Forecasting, 34, 635663, https://doi.org/10.1175/WAF-D-18-0184.1.

    • Search Google Scholar
    • Export Citation
  • Lee, T. R., M. Buban, and T. P. Meyers, 2021: Application of bulk Richardson parameterizations of surface fluxes to heterogeneous land surfaces. Mon. Wea. Rev., 149, 32433264, https://doi.org/10.1175/MWR-D-21-0047.1.

    • Search Google Scholar
    • Export Citation
  • Ma, M., Z. Pu, S. Wang, and Q. Zhang, 2011: Characteristics and numerical simulations of extremely large atmospheric boundary-layer heights over an arid region in north-west China. Bound.-Layer Meteor., 140, 163176, https://doi.org/10.1007/s10546-011-9608-2.

    • Search Google Scholar
    • Export Citation
  • Markowski, P. M., N. T. Lis, D. D. Turner, T. R. Lee, and M. S. Buban, 2019: Observations of near-surface vertical wind profiles and vertical momentum fluxes from VORTEX-SE 2017: Comparisons to Monin–Obukhov similarity theory. Mon. Wea. Rev., 147, 38113824, https://doi.org/10.1175/MWR-D-19-0091.1.

    • Search Google Scholar
    • Export Citation
  • Mauritsen, T., G. Svensson, S. S. Zilitinkevich, I. Esau, L. Enger, and B. Grisogono, 2007: A total turbulent energy closure model for neutrally and stably stratified atmospheric boundary layers. J. Atmos. Sci., 64, 41134126, https://doi.org/10.1175/2007JAS2294.1.

    • Search Google Scholar
    • Export Citation
  • McTaggart‐Cowan, R., and Coauthors, 2019: Modernization of atmospheric physics parameterization in Canadian NWP. J. Adv. Model. Earth Syst., 11, 35933635, https://doi.org/10.1029/2019MS001781.

    • Search Google Scholar
    • Export Citation
  • Meyers, T. P., 2001: A comparison of summertime water and CO2 fluxes over rangeland for well watered and drought conditions. Agric. For. Meteor., 106, 205214, https://doi.org/10.1016/S0168-1923(00)00213-6.

    • Search Google Scholar
    • Export Citation
  • Meyers, T. P., 2016: AmeriFlux BASE US-Aud Audubon Research Ranch, Ver. 4-1. AmeriFlux AMP, accessed 26 April 2023, https://doi.org/10.17190/AMF/1246028.

  • Oke, T. R., 1987: Boundary Layer Climates. 2nd ed. Routledge Press, 464 pp.

  • Olson, J. B., and Coauthors, 2021: A description of the MYNN surface-layer scheme. NOAA Tech. Memo. OAR GSL-67, 26 pp., https://doi.org/10.25923/f6a8-bc75.

  • Pal, S., 2016: On the factors governing water vapor turbulence mixing in the convective boundary layer over land: Concept and data analysis technique using ground-based lidar measurements. Sci. Total Environ., 554, 1725, https://doi.org/10.1016/j.scitotenv.2016.02.147.

    • Search Google Scholar
    • Export Citation
  • Pal, S., and M. Haeffelin, 2015: Forcing mechanisms governing diurnal, seasonal, and interannual variability in the boundary layer depths: Five years of continuous lidar observations over a suburban site near Paris. J. Geophys. Res. Atmos., 120, 11 93611 956, https://doi.org/10.1002/2015JD023268.

    • Search Google Scholar
    • Export Citation
  • Pal, S., M. Haeffelin, and E. Batchvarova, 2013: Exploring a geophysical process‐based attribution technique for the determination of the atmospheric boundary layer depth using aerosol lidar and near‐surface meteorological measurements. J. Geophys. Res. Atmos., 118, 92779295, https://doi.org/10.1002/jgrd.50710.

    • Search Google Scholar
    • Export Citation
  • Pal, S., T. R. Lee, and N. E. Clark, 2020: The 2019 Mississippi and Missouri River flooding and its impact on atmospheric boundary layer dynamics. Geophys. Res. Lett., 47, e2019GL086933, https://doi.org/10.1029/2019GL086933.

    • Search Google Scholar
    • Export Citation
  • Peel, M. C., B. L. Finlayson, and T. A. McMahon, 2007: Updated world map of the Köppen-Geiger climate classification. Hydrol. Earth Syst. Sci., 11, 16331644, https://doi.org/10.5194/hess-11-1633-2007.

    • Search Google Scholar
    • Export Citation
  • Pielke, R. A., Sr., 2001: Influence of the spatial distribution of vegetation and soils on the prediction of cumulus convective rainfall. Rev. Geophys., 39, 151177, https://doi.org/10.1029/1999RG000072.

    • Search Google Scholar
    • Export Citation
  • Prăvălie, R., 2016: Drylands extent and environmental issues. A global approach. Earth Sci. Rev., 161, 259278, https://doi.org/10.1016/j.earscirev.2016.08.003.

    • Search Google Scholar
    • Export Citation
  • Salesky, S. T., and M. Chamecki, 2012: Random errors in turbulence measurements in the atmospheric surface layer: Implications for Monin–Obukhov similarity theory. J. Atmos. Sci., 69, 37003714, https://doi.org/10.1175/JAS-D-12-096.1.

    • Search Google Scholar
    • Export Citation
  • Santanello, J. A., Jr., P. Lawston, S. Kumar, and E. Dennis, 2019: Understanding the impacts of soil moisture initial conditions on NWP in the context of land–atmosphere coupling. J. Hydrometeor., 20, 793819, https://doi.org/10.1175/JHM-D-18-0186.1.

    • Search Google Scholar
    • Export Citation
  • Sorbjan, Z., 2010: Gradient‐based scales and similarity laws in the stable boundary layer. Quart. J. Roy. Meteor. Soc., 136, 12431254, https://doi.org/10.1002/qj.638.

    • Search Google Scholar
    • Export Citation
  • Sorbjan, Z., 2017: Assessment of gradient-based similarity functions in the stable boundary layer derived from a large-eddy simulation. Bound.-Layer Meteor., 163, 375392, https://doi.org/10.1007/s10546-017-0234-5.

    • Search Google Scholar
    • Export Citation
  • Stensrud, D. J., R. L. Gall, S. L. Mullen, and K. W. Howard, 1995: Model climatology of the Mexican monsoon. J. Climate, 8, 17751794, https://doi.org/10.1175/1520-0442(1995)008<1775:MCOTMM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology. Kluwer Academic, 666 pp.

  • Sun, J., E. S. Takle, and O. C. Acevedo, 2020: Understanding physical processes represented by the Monin–Obukhov bulk formula for momentum transfer. Bound.-Layer Meteor., 177, 6995, https://doi.org/10.1007/s10546-020-00546-5.

    • Search Google Scholar
    • Export Citation
  • Valdebenito B, Á. M., S. Pal, G. Lammel, A. Behrendt, and V. Wulfmeyer, 2011: A novel approach for the characterisation of transport and optical properties of aerosol particles near sources—Part II: Microphysics–chemistry-transport model development and application. Atmos. Environ., 45, 29812990, https://doi.org/10.1016/j.atmosenv.2010.09.004.

    • Search Google Scholar
    • Export Citation
  • Wagner, T. J., P. M. Klein, and D. D. Turner, 2019: A new generation of ground-based mobile platforms for active and passive profiling of the boundary layer. Bull. Amer. Meteor. Soc., 100, 137153, https://doi.org/10.1175/BAMS-D-17-0165.1.

    • Search Google Scholar
    • Export Citation
  • Wilson, J. D., 2008: Monin-Obukhov functions for standard deviations of velocity. Bound.-Layer Meteor., 129, 353369, https://doi.org/10.1007/s10546-008-9319-5.

    • Search Google Scholar
    • Export Citation
  • Wulfmeyer, V., and Coauthors, 2018: A new research approach for observing and characterizing land–atmosphere feedback. Bull. Amer. Meteor. Soc., 99, 16391667, https://doi.org/10.1175/BAMS-D-17-0009.1.

    • Search Google Scholar
    • Export Citation
  • Wulfmeyer, V., and Coauthors, 2023: Estimation of the surface fluxes for heat and momentum in unstable conditions with machine learning and similarity approaches for the LAFE data set. Bound.-Layer Meteor., 186, 337371, https://doi.org/10.1007/s10546-022-00761-2.

    • Search Google Scholar
    • Export Citation
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  • Anand, M., and S. Pal, 2023: Exploring atmospheric boundary layer depth variability in frontal environments over an arid region. Bound.-Layer Meteor., 186, 251285, https://doi.org/10.1007/s10546-022-00756-z.

    • Search Google Scholar
    • Export Citation
  • Andreas, E. L., and B. B. Hicks, 2002: Comments on “Critical test of the validity of Monin–Obukhov similarity during convective conditions”. J. Atmos. Sci., 59, 26052607, https://doi.org/10.1175/1520-0469(2002)059<2605:COCTOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Benjamin, S. G., and Coauthors, 2016: A North American hourly assimilation and model forecast cycle: The Rapid Refresh. Mon. Wea. Rev., 144, 16691694, https://doi.org/10.1175/MWR-D-15-0242.1.

    • Search Google Scholar
    • Export Citation
  • Best, M. J., and Coauthors, 2011: The Joint UK Land Environment Simulator (JULES), model description—Part 1: Energy and water fluxes. Geosci. Model Dev., 4, 677699, https://doi.org/10.5194/gmd-4-677-2011.

    • Search Google Scholar
    • Export Citation
  • Beyrich, F., and Coauthors, 2002: Experimental determination of turbulent fluxes over the heterogeneous LITFASS area: Selected results from the LITFASS-98 experiment. Theor. Appl. Climatol., 73, 1934, https://doi.org/10.1007/s00704-002-0691-7.

    • Search Google Scholar
    • Export Citation
  • Businger, J. A., J. C. Wyngaard, Y. Izumi, and E. F. Bradley, 1971: Flux-profile relationships in the atmospheric surface layer. J. Atmos. Sci., 28, 181189, https://doi.org/10.1175/1520-0469(1971)028<0181:FPRITA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Carleton, A. M., 1985: Synoptic and satellite aspects of the southwestern U.S. summer ‘monsoon’. J. Climatol., 5, 389402, https://doi.org/10.1002/joc.3370050406.

    • Search Google Scholar
    • Export Citation
  • Dirmeyer, P. A., and Coauthors, 2012: Evidence for enhanced land–atmosphere feedback in a warming climate. J. Hydrometeor., 13, 981995, https://doi.org/10.1175/JHM-D-11-0104.1.

    • Search Google Scholar
    • Export Citation
  • Dowell, D. C., and Coauthors, 2022: The High-Resolution Rapid Refresh (HRRR): An hourly updating convection-allowing forecast model. Part I: Motivation and system description. Wea. Forecasting, 37, 13711395, https://doi.org/10.1175/WAF-D-21-0151.1.

    • Search Google Scholar
    • Export Citation
  • Eltahir, E. A. B., 1998: A soil moisture–rainfall feedback mechanism: 1. Theory and observations. Water Resour. Res., 34, 765776, https://doi.org/10.1029/97WR03499.

    • Search Google Scholar
    • Export Citation
  • Foken, T., 2006: 50 years of the Monin–Obukhov similarity theory. Bound.-Layer Meteor., 119, 431447, https://doi.org/10.1007/s10546-006-9048-6.

    • Search Google Scholar
    • Export Citation
  • Greene, B. R., S. T. Kral, P. B. Chilson, and J. Reuder, 2022: Gradient-based turbulence estimates from multicopter profiles in the Arctic stable boundary layer. Bound.-Layer Meteor., 183, 321353, https://doi.org/10.1007/s10546-022-00693-x.

    • Search Google Scholar
    • Export Citation
  • Hamel, M., 2022: Convective boundary layer turbulence profiling over an arid region using a 200m tall-tower and Doppler lidar measurements. M.S. thesis, Dept. of Geosciences, Texas Tech University, 143 pp., https://ttu-ir.tdl.org/bitstreams/f52ba1b4-95e1-42cd-b3d3-4f1d2bd7c8fc/download.

  • Hicks, B. B., 1978: Some limitations of dimensional analysis and power laws. Bound.-Layer Meteor., 14, 567569, https://doi.org/10.1007/BF00121895.

    • Search Google Scholar
    • Export Citation
  • Hicks, B. B., 1981: An examination of turbulence statistics in the surface boundary layer. Bound.-Layer Meteor., 21, 389402, https://doi.org/10.1007/BF00119281.

    • Search Google Scholar
    • Export Citation
  • James, E. P., and Coauthors, 2022: The High-Resolution Rapid Refresh (HRRR): An hourly updating convection-allowing forecast model. Part II: Forecast performance. Wea. Forecasting, 37, 13971417, https://doi.org/10.1175/WAF-D-21-0130.1.

    • Search Google Scholar
    • Export Citation
  • Jiménez, P. A., J. Dudhia, J. F. González-Rouco, J. Navarro, J. P. Montávez, and E. García-Bustamante, 2012: A revised scheme for the WRF surface layer formulation. Mon. Wea. Rev., 140, 898918, https://doi.org/10.1175/MWR-D-11-00056.1.

    • Search Google Scholar
    • Export Citation
  • Kelley, C. L., and B. L. Ennis, 2016: SWiFT site atmospheric characterization. SANDIA Tech. Rep. SAND-2016-0216, 82 pp., https://www.osti.gov/servlets/purl/1237403.

  • Kottek, M., J. Grieser, C. Beck, B. Rudolf, and F. Rubel, 2006: World map of the Köppen-Geiger climate classification updated. Meteor. Z., 15, 259263, https://doi.org/10.1127/0941-2948/2006/0130.

    • Search Google Scholar
    • Export Citation
  • Krishnan, P., T. P. Meyers, R. L. Scott, L. Kennedy, and M. Heuer, 2012: Energy exchange and evapotranspiration over two temperate semi-arid grasslands in North America. Agric. For. Meteor., 153, 3144, https://doi.org/10.1016/j.agrformet.2011.09.017.

    • Search Google Scholar
    • Export Citation
  • Krishnan, P., T. P. Meyers, S. J. Hook, M. Heuer, D. Senn, and E. J. Dumas, 2020: Intercomparison of in situ sensors for ground-based land surface temperature measurements. Sensors, 20, 5268, https://doi.org/10.3390/s20185268.

    • Search Google Scholar
    • Export Citation
  • Kumar, M., C. Mallik, A. Kumar, N. C. Mahanti, and A. M. Shekh, 2010: Evaluation of the boundary layer depth in semi-arid region of India. Dyn. Atmos. Oceans, 49, 96107, https://doi.org/10.1016/j.dynatmoce.2009.01.002.

    • Search Google Scholar
    • Export Citation
  • Lavi, A., D. K. Farmer, E. Segre, T. Moise, E. Rotenberg, J. L. Jimenez, and Y. Rudich, 2013: Fluxes of fine particles over a semi-arid pine forest: Possible effects of a complex terrain. Aerosol Sci. Technol., 47, 906915, https://doi.org/10.1080/02786826.2013.800940.

    • Search Google Scholar
    • Export Citation
  • Lee, T. R., and S. Pal, 2017: On the potential of 25 years (1991–2015) of rawinsonde measurements for elucidating climatological and spatiotemporal patterns of afternoon boundary layer depths over the contiguous US. Adv. Meteor., 2017, 6841239, https://doi.org/10.1155/2017/6841239.

    • Search Google Scholar
    • Export Citation
  • Lee, T. R., and M. Buban, 2020: Evaluation of Monin–Obukhov and bulk Richardson parameterizations for surface–atmosphere exchange. J. Appl. Meteor. Climatol., 59, 10911107, https://doi.org/10.1175/JAMC-D-19-0057.1.

    • Search Google Scholar
    • Export Citation
  • Lee, T. R., and T. P. Meyers, 2023: New parameterizations of turbulence statistics for the atmospheric surface layer. Mon. Wea. Rev., 151, 85103, https://doi.org/10.1175/MWR-D-22-0071.1.

    • Search Google Scholar
    • Export Citation
  • Lee, T. R., M. Buban, D. D. Turner, T. P. Meyers, and C. B. Baker, 2019: Evaluation of the High-Resolution Rapid Refresh (HRRR) model using near-surface meteorological and flux observations from northern Alabama. Wea. Forecasting, 34, 635663, https://doi.org/10.1175/WAF-D-18-0184.1.

    • Search Google Scholar
    • Export Citation
  • Lee, T. R., M. Buban, and T. P. Meyers, 2021: Application of bulk Richardson parameterizations of surface fluxes to heterogeneous land surfaces. Mon. Wea. Rev., 149, 32433264, https://doi.org/10.1175/MWR-D-21-0047.1.

    • Search Google Scholar
    • Export Citation
  • Ma, M., Z. Pu, S. Wang, and Q. Zhang, 2011: Characteristics and numerical simulations of extremely large atmospheric boundary-layer heights over an arid region in north-west China. Bound.-Layer Meteor., 140, 163176, https://doi.org/10.1007/s10546-011-9608-2.

    • Search Google Scholar
    • Export Citation
  • Markowski, P. M., N. T. Lis, D. D. Turner, T. R. Lee, and M. S. Buban, 2019: Observations of near-surface vertical wind profiles and vertical momentum fluxes from VORTEX-SE 2017: Comparisons to Monin–Obukhov similarity theory. Mon. Wea. Rev., 147, 38113824, https://doi.org/10.1175/MWR-D-19-0091.1.

    • Search Google Scholar
    • Export Citation
  • Mauritsen, T., G. Svensson, S. S. Zilitinkevich, I. Esau, L. Enger, and B. Grisogono, 2007: A total turbulent energy closure model for neutrally and stably stratified atmospheric boundary layers. J. Atmos. Sci., 64, 41134126, https://doi.org/10.1175/2007JAS2294.1.

    • Search Google Scholar
    • Export Citation
  • McTaggart‐Cowan, R., and Coauthors, 2019: Modernization of atmospheric physics parameterization in Canadian NWP. J. Adv. Model. Earth Syst., 11, 35933635, https://doi.org/10.1029/2019MS001781.

    • Search Google Scholar
    • Export Citation
  • Meyers, T. P., 2001: A comparison of summertime water and CO2 fluxes over rangeland for well watered and drought conditions. Agric. For. Meteor., 106, 205214, https://doi.org/10.1016/S0168-1923(00)00213-6.

    • Search Google Scholar
    • Export Citation
  • Meyers, T. P., 2016: AmeriFlux BASE US-Aud Audubon Research Ranch, Ver. 4-1. AmeriFlux AMP, accessed 26 April 2023, https://doi.org/10.17190/AMF/1246028.

  • Oke, T. R., 1987: Boundary Layer Climates. 2nd ed. Routledge Press, 464 pp.

  • Olson, J. B., and Coauthors, 2021: A description of the MYNN surface-layer scheme. NOAA Tech. Memo. OAR GSL-67, 26 pp., https://doi.org/10.25923/f6a8-bc75.

  • Pal, S., 2016: On the factors governing water vapor turbulence mixing in the convective boundary layer over land: Concept and data analysis technique using ground-based lidar measurements. Sci. Total Environ., 554, 1725, https://doi.org/10.1016/j.scitotenv.2016.02.147.

    • Search Google Scholar
    • Export Citation
  • Pal, S., and M. Haeffelin, 2015: Forcing mechanisms governing diurnal, seasonal, and interannual variability in the boundary layer depths: Five years of continuous lidar observations over a suburban site near Paris. J. Geophys. Res. Atmos., 120, 11 93611 956, https://doi.org/10.1002/2015JD023268.

    • Search Google Scholar
    • Export Citation
  • Pal, S., M. Haeffelin, and E. Batchvarova, 2013: Exploring a geophysical process‐based attribution technique for the determination of the atmospheric boundary layer depth using aerosol lidar and near‐surface meteorological measurements. J. Geophys. Res. Atmos., 118, 92779295, https://doi.org/10.1002/jgrd.50710.

    • Search Google Scholar
    • Export Citation
  • Pal, S., T. R. Lee, and N. E. Clark, 2020: The 2019 Mississippi and Missouri River flooding and its impact on atmospheric boundary layer dynamics. Geophys. Res. Lett., 47, e2019GL086933, https://doi.org/10.1029/2019GL086933.

    • Search Google Scholar
    • Export Citation
  • Peel, M. C., B. L. Finlayson, and T. A. McMahon, 2007: Updated world map of the Köppen-Geiger climate classification. Hydrol. Earth Syst. Sci., 11, 16331644, https://doi.org/10.5194/hess-11-1633-2007.

    • Search Google Scholar
    • Export Citation
  • Pielke, R. A., Sr., 2001: Influence of the spatial distribution of vegetation and soils on the prediction of cumulus convective rainfall. Rev. Geophys., 39, 151177, https://doi.org/10.1029/1999RG000072.

    • Search Google Scholar
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  • Prăvălie, R., 2016: Drylands extent and environmental issues. A global approach. Earth Sci. Rev., 161, 259278, https://doi.org/10.1016/j.earscirev.2016.08.003.

    • Search Google Scholar
    • Export Citation
  • Salesky, S. T., and M. Chamecki, 2012: Random errors in turbulence measurements in the atmospheric surface layer: Implications for Monin–Obukhov similarity theory. J. Atmos. Sci., 69, 37003714, https://doi.org/10.1175/JAS-D-12-096.1.

    • Search Google Scholar
    • Export Citation
  • Santanello, J. A., Jr., P. Lawston, S. Kumar, and E. Dennis, 2019: Understanding the impacts of soil moisture initial conditions on NWP in the context of land–atmosphere coupling. J. Hydrometeor., 20, 793819, https://doi.org/10.1175/JHM-D-18-0186.1.