1. Introduction
The planetary boundary layer (PBL) serves as the interface through which the land surface and atmosphere exchange mass and energy. Soil moisture, land use, and even irrigation can influence PBL moisture and energy budgets. Cloud formation and convective precipitation may be triggered by wet or dry soils depending upon levels of preexisting atmospheric stability and moisture (Ek and Mahrt 1994; Findell and Eltahir 2003; Ek and Holtslag 2004).
Because the PBL is the portion of the atmosphere that interacts directly with the surface, moisture and temperature in this layer has a direct impact on society. Heat waves and drought may be amplified by PBL feedbacks (Miralles et al. 2014, 2019; Schumacher et al. 2019; Wakefield et al. 2019; Christian et al. 2020; Benson and Dirmeyer 2021) and pose a threat to human health and agriculture. On the other hand, above-normal surface latent heat fluxes can lead to overland reintensification of tropical cyclones and associated excess precipitation (Emanuel et al. 2008; Arndt et al. 2009; Andersen and Shepherd 2014; Andersen et al. 2013; Wakefield et al. 2021a). Thus, our ability to forecast high-impact events is dependent upon our understanding of PBL moisture and heat budget evolution.
The daytime evolution of moisture, temperature, and depth of the convective boundary layer (CBL) is sensitive to the partitioning of the moisture and heat budget components, including entrainment of heat and moisture from the free troposphere, upward fluxes of latent and sensible heat from the land surface, and horizontal advection. The closure of CBL moisture and heat budgets remains a challenge, especially for observation-based studies, as regular observations of CBL budget components are limited. Yet, these observation-based studies provide a valuable source of “truth” for the evaluation of numerical models. One approach to the budget closure problem involves the use of mixing diagrams.
The accurate representation of land–atmosphere coupling in models is extremely important for weather and climate predictions. Understanding and quantifying the complex relationships and interactions between the atmosphere and land surface has been a focus within the Global Energy and Water Exchanges project (GEWEX) and other communities [see Santanello et al. (2018) for background]. One of the many methods used to understand these processes are mixing diagrams (MDs). MDs provide a method for describing CBL moisture and temperature budget evolution, and for quantifying the relative contributions of surface fluxes, advection, radiative heating, and entrainment (Betts et al. 1992; Santanello et al. 2009, 2011). The strength of this framework lies in its applicability to both observational and modeling-based land–atmosphere coupling studies, and in its ability to capture the coevolution of surface and atmospheric processes. Conversely, the framework (as defined by the publications above) relies on observations of the evolution of the 2-m potential temperature θ and specific humidity q to represent the evolution of the entire PBL moisture and energy budget, and thus, operates on the assumption that 2-m observations are representative of the entire mixed layer. The use of surface meteorological observations was motivated by the relative abundance of such observations in both space and time (Santanello et al. 2009). However, 2-m observations are obtained within the surface layer, which is often superadiabatic and thus the amplitude of their daytime values are often greater than that of well-mixed layer of the CBL. Using a more representative mixed-layer average temperature and humidity limits this framework’s applicability to only those locations where thermodynamic profiles of the atmosphere are obtained multiple times between sunrise and sunset, when the CBL can be considered well mixed.
In this study, we introduce a modification to the MD framework that better approximates closure of the CBL moisture and heat budgets. Thermodynamic profiles retrieved from the ground-based infrared spectrometer (IRS) observations allows us to quantify the mixed layer’s mean moisture and θ evolution. Recent work (Wagner et al. 2022) allows us to calculate the large-scale advection of water vapor and temperature from a small network of IRS and Doppler lidars. Thus, we can observe all of the terms in the mixed-layer equations, except for the entrainment term, which can now be estimated as the residual term. We also evaluate the MD framework using large-eddy simulation (LES). LES has the advantage of being able to provide internally consistent and complete fields, meaning that the mixed-layer equations close by definition. In this study, we use LES to test hypotheses, such as whether the evolution of 2 m values is a reasonable proxy of the wholistic evolution of the mixed layer. It is explicitly not the aim of this study to compare the details of the LES with the observations, as those results are strongly dependent on the initial and boundary conditions of the LES.
We then apply this modified MD approach to observations from the Department of Energy Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) site (Sisterson et al. 2016) to demonstrate its feasibility, showcase its advantages, quantify its uncertainties, and discuss the unique analyses enabled by this new methodology. The case chosen occurred on 8 August 2017; the motivation for selecting this particular case will be provided later in the paper.
2. Methodology and data
This section first describes the observational datasets and large-eddy simulation model used in this analysis, before going into a more detailed description of the MD method.
a. AERI
The Atmospheric Emitted Radiance Interferometer (AERI) is a ground-based IRS that measures downwelling spectral infrared radiation (3.3 ≤ λ ≤ 19 μm) at a frequency of approximately twice per minute and a spectral resolution of 0.5 cm−1 (Knuteson et al. 2004a). Two calibration blackbodies are viewed regularly, resulting in a radiometric accuracy better than 1% of the ambient radiance (Knuteson et al. 2004b). Thermodynamic profiles are retrieved from the spectral radiance observations using an optimal estimation-based retrieval algorithm called Tropospheric Remotely Observed Profiling via Optimal Estimation (TROPoe, formerly AERIoe; Turner and Löhnert 2014; Turner and Blumberg 2019). A key aspect of the optimal estimation framework is the ability to provide quantified uncertainties and a full error characterization for each retrieved variable. In the lower half of the well-mixed CBL, the typical uncertainty in the TROPoe retrievals is 0.4°C and 0.8 g kg−1 for temperature and moisture, respectively [Fig. 4b in Blumberg et al. (2017)]. These uncertainties can be propagated into the calculation of derived variables such as convective indices (Blumberg et al. 2017) and land–atmosphere coupling metrics (Wakefield et al. 2021b). The current study uses AERI thermodynamic retrievals collected at the central facility of the ARM SGP site during the 2017 Land–Atmosphere Feedback Experiment (LAFE; Wulfmeyer et al. 2018).
b. Raman lidar
The Raman lidar at the SGP site is a custom research-grade instrument designed for the ARM program to observe water vapor profiles throughout the diurnal cycle (Turner et al. 2016; Goldsmith et al. 1998). It transmits 300-mJ pulses of 355-nm light at 30 Hz and collects the backscattered energy at 355 nm (i.e., the elastic backscatter) and the rotational–vibrational Raman scattered returns from nitrogen (387 nm) and water vapor (408 nm) molecules. The ratio of the water vapor Raman return to the nitrogen Raman return is proportional to the water vapor mixing ratio. The maximum resolution of the data is 7.5 m and 10 s; however, the resolution of the derived water vapor data is typically 35 m and 10 min. Corrections are applied to account for system deadtime, solar background, differential attenuation associated with the wavelength differences between 408- and 387-nm wavelengths, and the differential near-field overlap of the two channels (Turner and Goldsmith 1999).
c. Augmentation of IRS retrievals with Raman lidar observations
The true vertical resolution of the IRS thermodynamic retrievals decreases with height (Turner and Löhnert 2014), which can complicate the use of these data for some analyses. To improve the vertical resolution, additional observations from active thermodynamic remote sensors, like Raman lidar observations, may be used to constrain retrievals (Turner and Blumberg 2019; Turner and Löhnert 2021), and are especially beneficial for improving estimates of water vapor within the PBL (Smith et al. 2021). Even so, additional instrumentation is costly. As such, we compare analyses of the evolution of daytime CBL heat and moisture budgets using only the AERI data in the TROPoe retrieval (herein denoted as AERI) and using both AERI and collocated Raman lidar data as input into TROPoe (herein AERI+rlid).
d. Surface flux observations: ECOR
Sensible and latent heat fluxes were obtained at 30-min intervals from the E14 Eddy Correlation (ECOR) flux measurement system at the ARM SGP site. Turbulent fluxes are derived from the 30-min averaged covariances of vertical velocity and scalar meteorological variables (Cook and Sullivan 2020). The E14 ECOR site is collocated with the central facility, where the AERI, Raman lidar, and radiosonde observations are made. Calibration uncertainties of approximately 5% for sensible heat flux (SHF) and 6% for latent heat flux (LHF) are expected within the ECOR system due to measurement accuracies within primary variables such as u, υ, and w wind components, as well as a shortfall of 10%–25% in observed fluxes (Cook and Sullivan 2020). A quality-controlled value-added product (QCECOR) was introduced to correct some of these shortfalls (Tang et al. 2019; Cook and Sullivan 2020), resulting in improvements to PBL budget closure. Surface fluxes from the QCECOR dataset are used in this study.
e. Surface flux observations: EBBR system
The Energy Balance Bowen Ratio (EBBR) method uses the energy balance equation to produce 30-min averages of sensible and latent heat fluxes. Contrary to the ECOR approach, the EBBR method results in a closed surface energy budget due to how the fluxes are derived, but these fluxes could be biased due to calibration uncertainties and a sensitivity to land-cover type (Tang et al. 2019). The EBBR method is best suited to homogeneous land cover and shorter vegetation (Wang and Dickinson 2012), such as grasslands. The E13 EBBR station is also collocated with the central facility. A calibration uncertainty of 10% can be expected for both sensible and latent heat fluxes observed with the EBBR (Campos and Sisterson 2016).
Depending on wind direction, the EBBR station may sample a different land-cover type than the nearby ECOR station (Tang et al. 2019). Both sites sample the same surface when the wind direction is northerly or northeasterly (Cook and Sullivan 2020; Tang et al. 2019). Given a primarily ENE surface wind direction during our 8 August 2017 case study, differences in fluxes due to land cover are expected to be minimal. Because of the strong correlation between spatial variability of the surface buoyancy flux and soil moisture (Desai et al. 2006), we investigated the variability of soil moisture using the 9 km soil moisture product from the Soil Moisture Active Passive (SMAP; Chan et al. 2018) satellite dataset. The SMAP observations on 9 August (as the satellite did not overfly the ARM site on 8 August) showed a uniform field of soil moisture in a circle with a 25 km radius around the SGP central facility, with soil moisture values ranging from 0.165 to 0.185 cm3 cm−3 (not shown). Therefore, observations from both the EBBR (E13) and ECOR (E14) sites are expected to be representative of surface fluxes around the central facility and were averaged together for this study.
f. LES
To complement the observational analysis, we used the MicroHH model (van Heerwaarden et al. 2017) to perform LES of the same case. LES is not used here to recreate observational results, but rather test observational hypotheses. The use of LES as a virtual test bed has the advantage that all relevant variables are available, in all spatial and temporal dimensions, that this data is internally consistent, and that the budgets have to close by definition, down to the discretization error. This complete (but not necessarily correct) dataset allows us to test the validity of our entrainment closure assumption, of the 2-m temperature and humidity as a proxy for the mixed-layer average, and of the use of individual profiles instead of horizontal averages. MicroHH is a fast large-eddy simulation model and has been validated against a wide range of standard cases, ranging from theoretical pipe flow and Rayleigh–Benard convection to clear and cloudy boundary layers. For our simulations, we use the anelastic approximation of the filtered Navier–Stokes equations, discretized with a second-order central differencing spatial scheme, and a fourth-order Runge–Kutta time integration method on an Arakawa C grid. Potential temperature and water vapor mixing ratio are carried as thermodynamic variables and are conserved for adiabatic processes.
Simulations were run with initial and boundary conditions based on ARM’s constrained variational analysis (VARANAL) dataset (Xie et al. 2004), including surface fluxes, large-scale advection and radiative tendencies, and subsidence. It is important to note that the VARANAL dataset is spatially averaged over the entire SGP domain, rather than from the one or two sites alone, meaning that it differs slightly from the values used in the observational analysis, which is based on observations at the SGP Central Facility.
In the vertical dimension, we employ a 15-m grid spacing over a uniform 4200-m domain, of which the top 500 m are a buffer layer to filter out gravity waves. In each horizontal direction, we use a 10-m grid spacing and a horizontal domain size of 10 240 m and periodic boundary conditions. The LES is run for 8 August 2017 from 0600 to 2200 LT. Horizontally averaged profiles are output every 5 min, as well as the output of 16 individual columns equidistantly placed across the domain. The nonaveraged values of the velocity and thermodynamic variables in these columns can be interpreted as a simple proxy for the profile observations.
The first term on the right-hand side represents the average large-scale forcing and includes both advection and the radiative tendencies (which we will show are small for this case) across the boundary layer (with depth zi). The second term describes the surface fluxes. The surface fluxes are defined as the fluxes at the surface divided by the total boundary layer depth. The third term represents the entrainment flux, and the final term the encroachment, which may be nonzero if the boundary layer height is nonstationary with time.
The budget closes for conservative scalars that are horizontally averaged over the entire domain, with a minor residual due to numerical differences between the internal LES model and the temporally sparser postprocessing. Such closure is not guaranteed if considering only a single column location, as point observations would do. To calculate the entrainment and encroachment terms from the single column, the covariance of the vertical velocity and scalar would be considered relative to a temporal average with a half-hour window. We plan to address the challenges of single column calculations in a subsequent paper.
g. Mixing diagrams
Mixing diagrams are used to estimate the role of individual PBL moisture and heat budget components on the daytime CBL evolution. These diagrams attempt to separate the contributions of heat and moisture from the surface, entrainment, and advection to the overall moisture and temperature composition of the boundary layer during daytime hours.
According to Betts et al. (1992), when zi is defined at the top of the capping inversion, or top of the entrainment zone, then
Regular observations of entrainment are difficult to obtain outside of field campaigns, and therefore, it is difficult to accurately quantify the role entrainment plays in daytime CBL evolution. The MD framework in Santanello et al. (2009) adapts the Betts (1992) formula to represent components of the daytime CBL budgets graphically. Given information about the coevolution of θ and q in the PBL as well as surface fluxes and advection, it is possible to then estimate the contribution of entrainment to the daytime CBL water and energy budget. Given the sensitivity of the relative sizes of the two entrainment terms to the definition of zi, and the challenges with measuring zi accurately (e.g., Duncan et al. 2022; Kotthaus et al. 2023), we will group the two terms into a single “entrainment” term for the rest of this paper.
Such an analysis requires both PBL heat and moisture budgets to be expressed in the same units. Thus, moisture and temperature variables are scaled by the latent heat of vaporization Lυ and the specific heat Cp, respectively, to ensure that both budgets are represented by the same units and magnitude (kJ kg−1). Thus, every term in Eq. (3) is first multiplied by Cp or Lυ, depending on if we are considering the energy or moisture budget.
The radiative heating term QR can be computed directly from the TROPoe-retrieved thermodynamic profiles and cloud properties. A multifilter rotating shadowband radiometer (MFRSR; Harrison et al. 1994) is collocated with the other instruments at the SGP site, and aerosol optical depth (AOD) can be retrieved from this instrument (Harrison and Michalsky 1994). On 8 August 2017, the mean AOD at 500 nm over the daytime hours was 0.40. We assumed the scale height of the aerosol was 2 km [as suggested by Turner et al. (2001)], single scatter albedo of 0.95, and an asymmetry parameter of 0.7. These data were used in the longwave and shortwave versions of the RRTM (Mlawer et al. 1997; Iacono et al. 2008) to compute profiles of total radiative heating rate in the CBL. The vertical average of the radiative heating rate is small; the total radiative heating of the mixed layer during the daytime hours was 0.68 K on 8 August.
h. Mixed-layer definition
In our mixed-layer approach, the daytime evolution of PBL moisture and temperature is computed from observed mixed-layer averages of the observed quantities rather than from 2-m observations. The mixed layer over which θ and q were averaged was defined as the layer between approximately 0.1zi and 0.5zi. The lower limit of this mixed layer was selected to avoid the surface layer, which is typically within the lowest 10% of the PBL, while the upper bound was chosen to prevent sampling of the entrainment zone. While 0.5zi is a conservative choice for a mixed-layer upper bound, the choice of this limit was motivated by the vertical resolution of the thermodynamic profiles retrieved from the AERI. Biases in retrieved q and θ profiles are minimal below 0.5zi, but above this level the biases increase rapidly (Blumberg et al. 2017). The impact of selecting 0.5zi as the upper limit will be evaluated later in this paper.
i. Graphical representation of budget terms: Coevolution of θ and q
The coevolution of heat and moisture within the daytime PBL is represented by a curve in which each point along the curve represents the heat and moisture content of the PBL at a given time. The traditional mixing diagram shows the 2-m specific humidity qsfc multiplied by Lυ as the abscissa and the 2-m potential temperature θsfc multiplied by Cp as the ordinate. In the revised methodology, we leverage thermodynamic profiles retrieved from the AERI to compute MD curves from the mixed-layer mean Cp〈θ〉 and Lυ〈q〉 instead.
j. Graphical representation of budget terms
k. Graphical representation of budget terms: Advection
Advection should be considered in the MD analyses, but it can be difficult to obtain from irregularly spaced observations, especially at multiple vertical levels required when using a mixed-layer mean approach. Recently, however, Wagner et al. (2022) used a Green’s theorem–based approach to compute advection from AERI retrievals and collocated Doppler lidars at the ARM SGP site. This was done by calculating a line integral of the mean conditions along the various sides of the polygon defined by the observation sites at its vertices to obtain scalar gradients from which advection was derived. The Doppler lidar horizontal wind data are derived using an optimal estimation method (Baidar et al. 2023), which provides wind profiles throughout the entire boundary layer. These wind profiles are interpolated to the vertical grid used in the TROPoe retrievals, and then each level is processed independently to provide the mean advection for temperature and humidity at that level. Uncertainties in the thermodynamic and kinematic profiles are propagated using a Monte Carlo sampling method. This approach provides information about advection at multiple vertical levels within the PBL and is used in the current analysis to support better quantification of moisture and energy budgets throughout the mixed layer. Thus, the advection components of the budget equations are obtained by multiplying the mean of the mixed-layer advection of each scalar by time step, then summing those observations over the total observation period.
The radiative heating vector is obtained by summing the product of the mixed-layer mean radiative heating rate (in kelvins per unit time) and time step for all time steps in the period. This total radiative heating for the period is then multiplied by Cp as this vector is only computed when considering the PBL heat budget.
Entrainment is estimated from the MD approach by subtracting the sum of the surface flux, radiative heating, and advection vectors from the total change vector. In other words, the entrainment terms are estimated as the residual of all other MD terms and are not computed directly. As mentioned above, while the budget equations show two entrainment terms, they are often grouped together and discussed as one within the MD framework.
The zi is an essential piece of information in the analysis as surface fluxes are scaled over the depth of the CBL, and the vertical averaging depends on zi. CBL heights were computed from AERI-retrieved profiles by taking the retrieved potential temperature at the surface and adding both the 1σ in uncertainty at that level and an additional 0.5 K. A parcel was then lifted dry adiabatically until it intersected the potential temperature profile, and this level was defined as the PBLH. Radiosonde-derived PBLH estimates were computed using the same procedure.
l. Case study selection
The primary assumptions of the MD framework are that there are no synoptic boundaries or convection, and very small cloud fractions, over the domain during the analysis time. Cases with large advection can be analyzed (since we have observations of the horizontal advection from the network of sites); however, we prefer to limit our analysis to cases where the advective fluxes are smaller than the surface fluxes since we are interested in land–atmosphere feedbacks. We selected 8 August 2017 to test the new methodology as it satisfied this initial criterion. Furthermore, the case was part of the larger Land–Atmosphere Feedback Experiment (Wulfmeyer et al. 2018), and as such, detailed observations from the land surface to the free atmosphere were collected throughout the SGP site. This included radiosondes launched at 1830 and 1910 UTC in addition to the routine 6-hourly radiosonde observations at the ARM SGP site (at 0530, 1130, 1730, and 2330 UTC).
We selected our analysis period to avoid significant overlap with the PBL morning and evening transitions. Angevine et al. (2001) defines onset of the daytime CBL as the period when the nocturnal inversion has eroded and surface-based turbulent eddies exceed 200 m. The algorithm that estimates the PBLH from the AERI-retrieved profiles has a default (minimum) height of 300 m, and as such, we will consider CBL onset as the time in which PBLH exceeds 300 m, and surface sensible heat fluxes are positive. To avoid inclusion of the evening transition when the boundary layer decouples from the surface, we consider 1) only those times when the PBLH is actively increasing or is quasi–steady state (when ∂zi/∂t > −0.25 km h−1) and 2) when upward surface sensible heat fluxes are positive.
Figure 1 shows that the period from 1400 to 2200 UTC satisfied these conditions for the PBLH derived separately from both the AERI and AERI+rlid retrievals. This corresponds to 0900–1700 local time (LT).
Cross sections of (a),(b) potential temperature and (c),(d) water vapor mixing ratio for (left) AERI and (right) AERI+rlid on 8 Aug 2017, from 2 h before the period analyzed to 2 h after. Local time is shown on the x axis. Vertical dashed white lines indicate the bounds of the period analyzed. Solid black lines are the PBL height zi, and dashed black lines are equal to 0.5zi.
Citation: Journal of Applied Meteorology and Climatology 62, 7; 10.1175/JAMC-D-22-0163.1
3. Application of mixing-diagram approaches to observations
Time-height cross sections from the AERI+rlid (Figs. 1b,d) show a well-mixed PBL throughout zi, particularly in q, whereas the AERI retrievals display a vertical gradient in q above 0.5zi (Fig. 1c). This can be explained by the AERI’s reduced vertical resolution with height (Blumberg et al. 2017). Our choice of mixed-layer bounds is supported by nearly identical q and θ for both AERI and AERI+rlid below 0.5zi (Fig. 1; dashed lines).
On average, the two retrievals (AERI vs AERI+rlid) produce nearly identical mixed-layer θ evolution and similar mixed-layer q evolution (Fig. 2a). The agreement between the two retrievals is also displayed via mixing diagrams in Fig. 3a. The AERI+rlid has a greater sensitivity to water vapor changes in the PBL and therefore displays slightly greater variation in q along the MD curve, yet both retrievals produce the same overall change in moisture and temperature from 1400 to 2200 UTC (Fig. 3a). Furthermore, nearly identical PBL depths (Fig. 2d) between the two retrievals produced indistinguishable differences in advection, surface flux, and radiative heating vectors. Thus, both AERI and AERI+rlid produced nearly identical estimates of entrainment flux magnitudes. The primary difference between the AERI and AERI+rlid estimates of entrainment arises from the greater uncertainty associated with AERI observations, particularly with respect to water vapor.
Time series of (a) mixed-layer mean potential temperature (red) and specific humidity (blue), with radiosonde derived mixed-layer values overlaid as crosses—note that the AERI and AERI+rlid temperatures are virtually identical; (b) 30-min-averaged surface fluxes, with sensible heat flux in gold and latent heat flux in green; (c) mixed-layer temperature (red) and moisture (blue) advection, where the hourly advection is shown with markers and thick lines and the accumulated (cumulative) advection at each step is shown by the dashed lines; and (d) the PBLH determined from the AERI (solid) and AERI+rlid (dashed) retrievals, overlaid with radiosonde-derived PBL heights.
Citation: Journal of Applied Meteorology and Climatology 62, 7; 10.1175/JAMC-D-22-0163.1
Mixing diagrams for (a) AERI and AERI+rlid data, where black curves represent the coevolution of mixed-layer mean specific humidity and potential temperature in energy units and gray curves show the coevolution of the 2-m specific humidity and potential temperature. The mixing diagrams are normalized to start at the origin at the beginning of the analysis period (t0). The cloud of points at the end of each of the observation vectors in (a) represent the distribution of probabilities for a given vector, coded by distance (in standard deviation) from the mean value of each vector. Green, red, orange, blue, and orange vectors represent surface fluxes, radiative heating, advection, and entrainment, respectively. (b) LES data. The horizontal dashed purple line in (a), with its error bars, is the water vapor entrainment computed from the collocated Raman and Doppler lidars; see the text for details.
Citation: Journal of Applied Meteorology and Climatology 62, 7; 10.1175/JAMC-D-22-0163.1
MD curves using 2-m values (instead of the mean mixed-layer values) are also shown in Fig. 3a and demonstrate the amplified daytime evolution of moisture and potential temperature that results from sampling within the superadiabatic surface layer. The 2-m MD curves are consistently warmer and moister than mixed-layer MD curves, with the initial t0 values being (31.3, 296.5) kJ kg−1 for the 2-m traces and (29.3, 296.1) kJ kg−1 for the mean-mixed-layer traces. These initial values were subtracted from the entire CBL trace for each, resulting in each MD being translated to the origin for the t0 time (Fig. 3a). This helps to illustrate that the total change in budget quantities also differs between 2-m and mixed-layer MDs. Warming is more pronounced within the 2-m curves, while overall drying is more pronounced for the mixed-layer curves. As such, the derived entrainment fluxes also differ in magnitude for the mixed-layer versus 2-m approaches. A similar MD analysis using the LES data as input was created (Fig. 3b), but in this case the entrainment flux was directly computed from the LES output (i.e., it was not computed as a residual). Notice that the evolution of the CBL in the LES output qualitatively is the same as that shown by the observations and provides the same conclusions; namely, that the 2-m data does not result in closure of the heat and moisture budget but that using the mean mixed-layer values does.
The uncertainties in the various observations are also illustrated in the mixing diagram shown in Fig. 3a. The TROPoe retrievals have an error covariance matrix that is sampled using Monte Carlo techniques to generate a “point cloud” around the first and last points of the diurnal time period, with the color of the points indicating the percentage of the standard deviation of the retrieval uncertainty (as shown by the color bar). Similarly, the uncertainties provided by the advection product, and uncertainties in the surface fluxes and the PBL height (which define the surface vector contribution), are sampled the same way. As the entrainment is computed as a residual, the uncertainties from all of these components (i.e., the total vector, advection vector, and surface vector) are propagated to provide uncertainties in the entrainment vector.
The LES output was analyzed using two different thicknesses for the mixed-layer to test the sensitivity of using 0.5zi as the upper limit for the observations. Figure 4 shows that the evolution of the CBL is qualitatively identical when the mean values for the mixed layer were computed for the layer from 0.1zi to 0.5zi and when the mixed-layer means were computed over 0.1zi to 0.9zi, with the differences in the energy and water vapor evolution being less than 0.1 and 0.3 kJ kg−1, respectively, with marginally better closure for the results that used 0.9zi as the upper threshold. This result, together with the closure demonstrated by the LES results in Fig. 3b and the agreement with the observations in Fig. 3a, provides confidence that the CBL evolution observed by the AERI is well founded.
As in Fig. 3b, but these mixing diagrams show the evolution of the CBL from the LES if the maximum height used in the analysis is (a) 0.5zi or (b) 0.9zi.
Citation: Journal of Applied Meteorology and Climatology 62, 7; 10.1175/JAMC-D-22-0163.1
A comparison with mixed-layer (0.1zi to 0.5zi) mean values derived from afternoon radiosondes at 1730, 1830, and 1910 UTC shows that both AERI and AERI+rlid produced realistic mixed-layer mean θ values (Fig. 2a), but both remote sensing approaches observed a slightly moister mixed layer than the radiosonde. This might be explained by a potential dry bias in radiosondes (e.g., Turner et al. 2003); however, this was not investigated further here. Regardless, the pattern of evolution was similar, lending confidence to our use of the AERI and AERI+rlid for this analysis, as well as the MD vectors derived from these retrievals. While AERI and AERI+rlid PBLH were slightly greater than PBLH derived from radiosondes, they differed from radiosonde observations by no more than 250 m.
Entrainment fluxes can be difficult to observe, typically requiring either aircraft (e.g., Couvreux et al. 2007; Canut et al. 2012) or lidar systems (e.g., Träumner et al. 2011; Wulfmeyer et al. 2016). One consequence of the MD framework is the ability to estimate the entrainment fluxes by quantifying all other PBL budget components and computing the entrainment as a residual. Minimizing uncertainty in derived entrainment estimations is critical, and it is important to consider how each of the PBL components contribute to this uncertainty.
The surface flux vector is derived by normalizing surface fluxes over the depth of the PBL; therefore, its uncertainties arise from the uncertainties in zi and the surface flux observations. Even with multiple sources contributing to variability in the surface flux vector magnitudes, it contributes the least uncertainty toward the moisture budget (Fig. 5). Though both moisture advection and the moisture component of the AERI total vector have similar standard deviations, the uncertainty in moisture advection is approximately 50% of the mean (Fig. 5). Within the heat budget, uncertainty in advection, surface fluxes, and the total vectors are similar, with 1σ uncertainties being less than 0.5 kJ kg−1. As with the moisture budget, temperature advection uncertainties are greatest with respect to its mean value.
Vector magnitudes and uncertainties from the observational data. As in Fig. 3, the scattered points indicate the uncertainty in the vectors, and 1σ and 2σ contours are shown. Thick lines represent AERI-only MD values, whereas thin lines represent AERI+rlid values. The point cloud (uncertainty) for the entrainment vector was computed by propagating the uncertainty of the other components.
Citation: Journal of Applied Meteorology and Climatology 62, 7; 10.1175/JAMC-D-22-0163.1
Radiative heating plays a much smaller role than all budget components in this analysis, even though the aerosol optical depth was reasonably large (0.4 at 500 nm). Uncertainties associated with radiative heating may be considered negligible in comparison with other sources for this particular analysis; this same conclusion was reached by Santanello et al. (2005). The uncertainties in the entrainment vector are dominated by the result of uncertainties in total, advection, and surface flux vectors.
Uncertainties in moisture entrainment were greater than those for entrainment of heat, consistent with the greater uncertainties observed in other components of the moisture budget (in contrast to uncertainties in the heat budget). Even so, the standard deviations for both the moisture (1 kJ kg−1) and heat (0.3 kJ kg−1) components are approximately 15% of their respective means.
Water vapor entrainment flux can be observed using a combination of water vapor Raman lidar and Doppler lidar (Wulfmeyer et al. 2016), both of which operated during LAFE at the SGP site. Profiles of water vapor flux were computed from this matched lidar dataset at 30 min resolution on this day (C. Senff 2021, personal communication). Entrainment fluxes were computed from this lidar dataset by subtracting the mean water vapor flux between 0.75zi and 0.90zi from the mean flux between zi and 1.15zi; uncertainties in the lidar entrainment flux were propagated from the flux profile data. The lidar-derived water vapor entrainment flux (magenta line, Fig. 3a) was slightly greater than that of the mixed-layer MD-derived entrainment flux value. However, the uncertainty ranges overlapped for each of the two estimates suggesting we can trust the MD-derived entrainment flux.
4. Non-steady-state convective boundary layer
MD vectors represent time integrated PBL budget terms, representing the accumulated contribution of PBL budget components from t0 to tf. In some instances, however, it may be important to consider variability in budget terms over a shorter time window than the entire daytime period. Figure 6 shows mixing diagrams for the first (0900–1300 LT) and second (1300–1700 LT) halves of the daytime period based on the remote sensing observations (Figs. 6a,b) and LES (Figs. 6c,d). Despite initially smaller surface flux magnitudes in the morning than in the afternoon (Fig. 2b), the morning period showed slightly greater warming in the CBL, associated with a larger overall surface flux contribution. This can be explained by a shallower PBL depth over which the surface fluxes were distributed during the first half of the day. Moreover, the 2-m MD curves demonstrate the sensitivity to the surface layer, as they overestimate the amount of warming in the morning, yet slightly underestimate warming in the afternoon. This would lead to an overestimation of entrainment heat flux in the morning and slight underestimation in the afternoon when compared with the mixed-layer mean curves. Similar levels of PBL drying were also observed between the two periods, though the larger surface flux vector and smaller advection vector in the first half of the day, indicated a greater contribution of entrainment toward the moisture budget.
As in Fig. 3, but these mixing diagrams show the evolution in the (left) morning (0900–1300 LT) and (right) afternoon (1300–1700 LT) derived from (a),(b) the observations and (c),(d) the LES.
Citation: Journal of Applied Meteorology and Climatology 62, 7; 10.1175/JAMC-D-22-0163.1
The ability to examine the morning and afternoon periods independently allows us to consider how the three factors (surface, entrainment, and advection) influenced the evolution of the CBL in the two periods. It also allows us to examine whether similar levels of drying between the morning and afternoon were due to similar relative contributions of advection, surface fluxes, and entrainment throughout the period, or if one PBL budget component was more important in the morning than in the afternoon. Analysis of morning versus afternoon may also aid in identifying the role of entrainment on the CBL evolution during early PBL growth into a residual layer, if and when one is present. Ultimately, we desire to use this ability to evaluate how well PBL schemes in numerical weather prediction and climate models represent the evolution of the convective boundary layer. In this case, there was no canonical residual layer present, though a drier layer between 0.5 and 1 km was observed in the AERI+rlid cross section (Fig. 1d) before 1300 LT.
5. Conclusions
In this work, we explored using ground-based remote sensors to monitor the evolution of the moisture and heat budgets of the convective boundary layer using mixing diagrams. In particular, we demonstrated several things. First, using LES output, we showed that CBL moisture and temperature budget closure is more likely to be achieved through use of mixed-layer mean quantities; using the 2-m observations as is traditionally done does not yield closure (Fig. 3b). Additionally, the LES analysis demonstrated that the closure is nearly identical when the mean mixed-layer quantities were computed over the 0.1zi to 0.5zi layer relative to the 0.1zi to 0.9zi layer (Fig. 4). These results do not mean that using 2-m observations in the mixing diagram is not useful for evaluating models against observations; however, if the focus is on accurate estimates of entrainment and other CBL budget components then using mixed-layer mean values is essential.
Second, an important aspect of this work is that the temperature and moisture advection was directly measured using a network of AERI and Doppler lidar systems. Many previous MD analyses have assumed that the advection is zero; however, with direct measurements of advection as shown here, the MD framework can be used to evaluate land–atmosphere interactions for a range of advection values.
Third, temporally resolved thermodynamic profiles throughout the daytime period are needed for a MD analysis, and we demonstrated that the ground-based AERI is able to provide the needed thermodynamic profiles and zi observations. The AERI thermodynamic profiles provide qualitatively the same mixed-layer PBL evolution as the higher information content AERI+rlid profiles (Fig. 3a), thus demonstrating that the observations from the Raman lidar are not required. However, because of the lower vertical resolution of the AERI-retrieved profiles, we recommend that the mixed-layer mean values are derived only over the bottom portion of the mixed layer (i.e., from 0.1zi to 0.5zi). (Other passive remote sensors, such as multichannel microwave radiometers, could potentially be used in a similar manner as the AERI, but some work would need to be done to select the correct height range over which to compute an unbiased estimate of the mixed-layer mean temperature and humidity.)
A strength of the MD methodology, using the AERI-retrieved profiles, is that the entrainment fluxes at the top of the CBL can be derived as a residual. Observations of the entrainment at the top of the CBL are challenging and thus relatively rare; this MD-based approach has the potential to provide a large dataset collected in a range of different locations. In our case study, there was good agreement in the entrainment flux derived as a residual from the observations with that computed directly from the LES (Fig. 3a vs Fig. 3b). Furthermore, although it was only a single case, the agreement with the water vapor entrainment flux derived from the combination of the Raman lidar and Doppler lidar showed agreement with the AERI-derived entrainment flux within the combined uncertainties. The entrainment ratio, computed from the entrainment relative to the surface flux, is similar to past observational studies such as Angevine et al. (1998) and Betts et al. (1990, 1992), lending confidence to our methodology.
The MD approach has a few limitations. It assumes that, over the analysis period, that there are no synoptic boundaries that pass over the site. Also, as implemented here, latent heating from phase change (e.g., cloud formation or precipitation) is not accounted for in the analysis, and thus precipitating periods should be avoided. In addition, if the emphasis is to evaluate land–atmosphere interactions, then we recommend that the cases be selected such that the horizontal advective fluxes are less than the surface fluxes. An on-going study using MDs to evaluate the High-Resolution Rapid Refresh (HRRR) model (Dowell et al. 2022) analyzed a 3-month period from May to July 2019 and found that 30 cases satisfied the constraints of the method; this study will be the subject of a future paper.
The high temporal resolution of the AERI enables the evaluation of smaller time periods within the daytime CBL. This is a valuable tool for identifying relative contributions of each budget component when advection may change throughout the day, or when we are interested in knowing how budget components change based on whether the PBL is actively deepening or in steady state. For example, if a pronounced residual layer were present, the effects of entrainment fluxes may appear more pronounced during the morning period while the PBL is deepening. Similarly, this approach could provide new insights into the morning and afternoon-to-evening transitions. The ability to examine smaller periods of time is also critical for model evaluation purposes. We can determine whether CBL budget evolution is better simulated during certain times of day, and whether simulated budget components display better agreement at certain times. Though observations are often considered truth, they are imperfect. By including uncertainty in our observation-based mixing diagrams, we can perform model evaluation with better objectivity, noting whether model representation of CBL budget components and their evolution may still be within an observational window of uncertainty.
An important implication of this work is that a combination of an infrared spectrometer (IRS) and a surface turbulent flux station is able to characterize the energy and moisture budget of the convective boundary layer; additional instruments are not required if the advection can be assumed to be negligible. IRS instruments have been deployed in long-duration fixed sites (e.g., the ARM SGP, where AERIs are located both in pasture and cropland locations) and in shorter field campaigns ranging from the tall forests of Wisconsin (Butterworth et al. 2021) to the U.S. Southeast (Wagner et al. 2019) to the Sahel (Turner 2008). These datasets will be used to better understand the influence of land–atmosphere coupling during the daytime (and shorter time window) CBL evolution over a range of land-use types.
An important and novel contribution of this study is the inclusion of observed advection into the MD analyses. It is difficult to obtain advection from observations, especially advection throughout the PBL, but the network of AERIs and Doppler lidars at the ARM SGP provides a unique opportunity to do so. As such, we can further disentangle PBL budget components to better differentiate the role of entrainment on PBL evolution. Without the inclusion of advection observations, the residual vector would include information about both advection and entrainment. Last, we can determine which days are most likely to be influenced by local land–atmosphere coupling from observations, using the advective flux ratio as suggested by Santanello et al. (2009).
Acknowledgments.
This work was supported by the Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) via a grant to the Global Systems Laboratory, the DOE Atmospheric System Research (ASR) program (Grants 89243019SSC000034 and DE-SC0020114), the Future Investigators in NASA Earth Space Science and Technology (FINESST) program via award 80NSSC19K1365, and the NOAA Atmospheric Science for Renewable Energy (ASRE) program. We thank Dr. Christoph Senff for providing the water vapor flux profiles from the combined Raman and Doppler lidars that was used to derive a comparison of the water vapor entrainment rate on this day, and Dr. Siwei He for providing comments on an earlier version of this paper.
Data availability statement.
The observational data used in this analysis are stored in the ARM data archive (https://arm.gov; click on the “data” tab). The LES model was driven with the variational analysis data product, which is also in the ARM data archive. The LES output can be requested from the authors.
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