## 1. Introduction

The southeastern Pacific atmospheric boundary layer has been the focus of intensive study over recent years because of its importance in Earth’s climate system (de Szoeke and Xie 2008). The region is characterized by strong ocean upwelling, cool sea surface temperatures (SSTs), and an extensive stratocumulus cloud sheet that reflects much more solar energy to space than the underlying ocean. The coastal region is also a strong source of anthropogenic particulate matter so there exists the potential for aerosol–cloud interactions that could modify cloud microphysics and precipitation formation, with further implications for cloud reflectance.

A recent field experiment, Variability of the American Monsoon Systems (VAMOS) Ocean–Cloud–Atmosphere–Land Study—Regional Experiment (VOCALS-REx; Wood et al. 2011) deployed multiple aircraft and ships to study the coupled ocean–atmospheric boundary layer system. The experiment was designed to address the key science issues of ocean–atmosphere coupling and the role of the aerosol in modifying cloud microphysics, precipitation, and cloud forcing. During VOACLS-REx, the National Oceanic and Atmospheric Administration (NOAA) Research Vessel (R/V) *Ronald H. Brown* (*RHB*) was outfitted with a suite of measurements to characterize, inter alia, the thermodynamics, dynamics, and microphysics of the cloudy marine boundary layer. The *RHB* spent a total of 63 days in the southeastern Pacific, focusing primarily on latitude 20°S (±1°), between 70° and 85°W. It was equipped with a large number of in situ and remote sensing instruments to measure SST, surface fluxes, atmospheric state, aerosol size, composition and optical properties, and cloud and drizzle [for a full list of instruments, see Wood et al. (2011, their Table 3)]. Radiosondes were launched at 4-h intervals. The focus of this paper will be on the scanning, NOAA high-resolution Doppler lidar (HRDL; Tucker et al. 2009) that provided continuous measurements of the dynamics of the boundary layer through measurement of the radial wind velocity, as well as aerosol-backscatter signal intensity along the lidar’s line of sight (LOS). Together with some of the other key instruments such as the NOAA C-band precipitation radar (Comstock et al. 2004; Mechem et al. 2012); the microwave radiometer, which provided measurements of cloud liquid water path (LWP; Zuidema et al. 2005); and the NOAA W-band radar (Moran et al. 2012), the *RHB* cruise yields an unprecedented view of the dynamics of the cloudy marine boundary layer over a range of SSTs, boundary layer depths, aerosol conditions, and over many diurnal cycles. Key to this is the fact that the instruments sampled the boundary layer continuously and at high temporal frequency.

Models of different levels of complexity have been developed and applied to the stratocumulus-capped marine boundary layer. These include mixed-layer models (e.g., Lilly 1968; Schubert 1976), one-dimensional turbulence closure models (e.g., Mellor and Yamada 1974; Bougeault 1985; Chen and Cotton 1987), and large-eddy simulation (LES; e.g., Deardorff 1972; Moeng 1986; Mason 1989). LES is probably the most appropriate numerical tool to address processes associated with the turbulent cloudy boundary layer but the computational challenge is to do so with fine-enough resolution and large-enough domain size. For small horizontal domains on the order of 3 × 3 km^{2}, horizontal grid spacing ^{2} domain with *O*(^{2}) size for the *O*(10 h) durations typically used by LES studies.

One of the motivations for near-LES derives from the scales of mesoscale organization in marine boundary layer cloud fields. Based on satellite data Wood and Hartmann (2006) found that the horizontal-to-vertical-scale aspect ratio of mesoscale cellular convection for the marine cloudy boundary layer greater than 1 km is typically in the 30:1 to 40:1 range. Based on power spectral density (PSD) analysis, de Roode et al. (2004, hereafter DDJ04) concluded that a sufficiently large domain size is necessary to manifest scalar variance for stratocumulus simulation. The spectral peak for scalar variables appears at a wavelength of approximately *w* is at approximately 1 km. Thus, while choice of resolution is unarguably important, the scales of mesoscale organization suggest that the choice of domain size may be of equal importance. We will test the sensitivity of the simulated turbulence to domain size for the Advanced Research Weather Research and Forecasting Model (ARW) and compare ARW trends to those in the evaluation of modeled turbulence by DDJ04.

Although the community ARW model was not necessarily developed with LES application in mind, it has increasingly been applied in LES or near-LES mode (e.g., Moeng et al. 2007; Wang and Feingold 2009a,b; Feingold et al. 2010; Kazil et al. 2011; Solomon et al. 2011; Blossey et al. 2013) and therefore it behooves the community to evaluate its performance, not only against other LES models, but equally importantly, against observations. ARW has been tested on several LES intercomparison cases of the Global Atmospheric System Studies (GASS, formerly GCSS) (Stevens et al. 2005, hereafter S05; Ackerman et al. 2009; vanZanten et al. 2011) and the results have been shown to compare reasonably well with other models (Wang et al. 2009; Yamaguchi and Feingold 2012, hereafter YF12). Comparison with observations is thus timely.

The robustness of LES-generated turbulence can be assessed within the modeling framework alone (e.g., Matheou et al. 2011), which is an essential step, especially when testing newly developed model and/or numerical schemes. Another approach is model evaluation with well-defined turbulence measurements such as those made by lidar (e.g., Mayor et al. 2003; Lenschow et al. 2012). In the current study, the dataset produced during VOCALS-REx represents significant opportunity for model comparison with observations.

The objectives of this study can be described as 1) simulation of a nonprecipitating stratocumulus case with the ARW based on ship measurements during VOALS-REx, 2) development of a framework for comparison between model and observation, 3) evaluation of model-simulated turbulence with lidar observations, and 4) evaluation of the influence of the ARW configuration on the quality of the comparison. For the modeled turbulence evaluation, we focus primarily on Doppler lidar observations of (i) *w* statistics, including

To accomplish these objectives, we will present results from one LES and three near LESs. Three square domains with horizontal length *L* of 6.4, 12.8, and 25.6 km are used. For LES of stratocumulus, ARW tends to be more expensive compared to large-eddy models formulated with the anelastic system (YF12). For the worst case, ARW is about 20 times more expensive than an anelastic counterpart. We use

Comparison between model and observation is not an easy task. A few of the key issues are outlined below. (i) While turbulence exists in nature at the simulation start time, LES is traditionally initialized in a quiescent state with pseudorandom perturbation to drive turbulence. It is well known that the LWP decreases in response to the first large-eddy turnover (e.g., Moeng et al. 1996; S05) so that the state when turbulence is fully spun up may have already diverged from the observed state. (ii) Frequently horizontal average LES quantities are used for comparison to observations, whereas the ship-based measurement is a two-dimensional “curtain” that advects in time owing to the relative speed of the ship and the mean wind, so that the statistics are derived based on a temporal analysis. Directly comparing these two different statistics has the potential to be misleading and will be investigated here. (iii) Although our objective is not a forecast of the system evolution, a subset of the model parameters should compare well to observations for turbulence comparison to be meaningful. Reasonable adjustments to the initial soundings and forcings have to be carefully considered. Keeping simplicity in mind, we develop a methodology for model comparison with observation, especially for turbulence, that we believe will be broadly beneficial for other model–observational comparisons.

The outline of this paper is as follows. The lidar and data characteristics are described in the next section. A brief description of ARW and our configuration of the dynamical core and physics is summarized in section 3. A case description of a nonprecipitating nocturnal stratocumulus based on ship measurements during VOCALS-REx is discussed in section 4. The details of our framework for model comparison with observation are presented in section 5. The model evaluation is carried out in section 6. We discuss additional sensitivity tests in section 7. A summary is given in section 8.

## 2. Lidar observation and data

NOAA’s HRDL was deployed on the *RHB* during VOCALS-REx to monitor *μ*m, solid-state laser operated with a repetition frequency of 200 Hz. Multiple atmospheric returns were combined to measure the LOS wind speed and aerosol-backscatter signal strength twice per second with an along-beam resolution of 30 m. Depending on aerosol concentration, HRDL typically made these measurements horizontally out to distances of 6–8 km and vertically through cloud base.

The pointing of the lidar was controlled with a motion-stabilized hemispheric scanner. During its normal operation, HRDL performed both azimuthal and elevation scans and stared vertically. When operated from a moving platform, the pointing of the system was actively maintained in the world frame to within 0.5° of the predefined scan parameters. This allowed for lidar measurements within 1° of elevation off the ocean surface or stabilized at zenith under moderate sea-state conditions. Information about the ship’s translational and rotational motion, supplied by the compensation system, was used to estimate and remove the effect of the platform motion from the LOS wind speed measurements. The precision of the LOS wind speed measurements depended in part on the strength of the atmospheric return but was typically 10–25 cm s^{−1} for the conditions encountered during VOCALS-REx.

HRDL operated continuously during the two research legs of the VOCALS-REx cruise, employing a 20-min repeating scan sequence that consisted of 10 min of azimuthal and elevation scans followed by 10 min of vertically staring measurements. The scanning data were combined to estimate profiles of *w* statistics from within 170 m of the ocean surface through the depth of the subcloud layer and up to the cloud. The quality of the statistics depends on the number of points sampled during the 10-min averaging period, both of which decrease in the vicinity of cloud base. This tends to result in a decrease in

From every 20-min sequence of data, single estimates of these profiles were calculated. These profiles form the basis for model evaluation. A caveat of the measured statistics is that they represent the variation over spatial scales up to approximately 3–4 km owing to the 10-min sampling period for *w* and the horizontal distance between the closest and farthest points at each level converted from the LOS for

## 3. Model description

The ARW, version 3.3.1, with the LES and statistics packages developed by YF12 is used for this study. ARW is a nonhydrostatic model, which solves the compressible system of equations in a flux form governed by a mass vertical coordinate. The basic prognostic variables are the zonal, meridional, and vertical velocities (*u*, *υ*, *w*); dry air mass; geopotential; and potential temperature

A time-split integration scheme, which separates the high-frequency acoustic and gravity waves from the low-frequency physical mode, is used for temporal discretization (Klemp et al. 2007). ARW uses a third-order Runge–Kutta scheme, and during each Runge–Kutta step, the horizontally propagating high-frequency mode is integrated with a forward–backward scheme with the acoustic time step, while an implicit scheme is used for the vertically propagating high-frequency mode. YF12 reported that simulation results exhibit a dependency on the acoustic Courant number associated with the acoustic time step. Additional discussion for the sensitivity on the acoustic time step is presented in appendix B.

The staggered Arakawa C grid is employed for spatial discretization. Advection is computed with a scheme described in Wicker and Skamarock (2002). As recommended in the ARW user’s guide, we select the fifth-order scheme for the horizontal advection and the third-order scheme for the vertical advection. For scalar advection, except

The following physical parameterizations are selected among the available schemes. A 1.5-order TKE closure (Klemp and Wilhelmson 1978; Deardorff 1980) is used as an SGS turbulence parameterization. Longwave radiative flux is computed with the Rapid Radiative Transfer Model (RRTMG) scheme (Mlawer et al. 1997) and updated every 30 s. This update period is appropriate for nocturnal stratocumulus simulations with

## 4. Nonprecipitating nocturnal stratocumulus case

### a. Physical setup

Examining the sonde and lidar data throughout the period of the *RHB* deployment in the VOCALS-REx region, we sought a nocturnal, well-mixed boundary layer structure (Lilly 1968) without precipitation, and selected 18 November 2008, when the ship was located at 19°S, 80°W. The sonde launch at 0336 UTC (2216 local time) was selected as the initialization time. The duration of simulations is 6 h and 24 min so that it finishes at 1000 UTC (0430 local time before sunrise). During this period, the ship travels 0.3°W and stays on 19°S, which translates to an average ship velocity of ^{−1}.

The observed and initial model soundings are shown in Fig. 1. A detailed description of the procedure to create the input profiles and data is given in appendix A. The figure also shows the

For the large-scale subsidence, a constant divergence of *D* between 1.3- and 2-km levels (free atmosphere) of the European Centre for Medium-Range Weather Forecasts (ECMWF) operational data. Lower boundary conditions (i.e., SST, sensible and latent heat fluxes, and friction velocity) are derived from the hourly averaged surface measurements (de Szoeke et al. 2010). These parameters are linearly time interpolated to the current time. To represent synoptic-scale motion, the Coriolis force at 19°S is applied. Although the simulations are performed in an Eulerian framework, we choose not to apply large-scale advective tendencies for

The two-moment microphysics scheme (Feingold et al. 1998) requires representation of the aerosol size distribution. It assumes a lognormal aerosol size distribution, which is a good approximation to the observed aerosol size distribution (Fig. 2). Analysis of the aerosol data shows that for the specific time period under consideration, the ratio of the two lognormal modal concentrations [^{−2}.

### b. Set of simulations

All simulations use a square domain with periodic lateral boundary condition and a domain depth of 2 km. The following set of simulations are performed and listed in Table 1: 6B, our base case, uses *w* (e.g., Fig. 10) with 6H shows that the wavelength of

List of the named simulations.

Strictly speaking, even the grid spacings of 6H may not be an LES because the major premise of LES is that the grid spacing is sufficiently small to fit well in the inertial subrange, and the simulation is relatively insensitive to the SGS parameterization (e.g., Moeng 1984; Bryan et al. 2003). Convergence of results with finer grids is of interest (e.g., Matheou et al. 2011) but beyond the scope of this study.

Following YF12, the physical time step

Throughout the study, model analyses are performed based on horizontal domain-averaged statistics recorded every minute and three-dimensional snapshot data saved every 10 min. The variables

## 5. Framework for a model comparison with observation

### a. Initial turbulence in quasi steady state with initial fields

Traditionally, LES is initialized with an observed cloudy boundary layer sounding but the model is in a quiescent state. Here, special effort is made to allow the model to generate initial turbulence that is in a statistically stationary state based on the initial cloudy profile. Establishing the turbulence associated with the initial observed cloud field is essential in order to compare with the time-evolving lidar-observed turbulence.

Our strategy is to apply a nudging technique to maintain the horizontal mean of *u*, *υ*,

A suite of experiments based on 6B shows that the existing PBL-top wind shear evaporates cloud, and that the effect is large in the wake of the first large eddy. This point was noted in Wang et al. (2012) for the Coupled Ocean–Atmosphere Mesoscale Prediction System–LES model (Golaz et al. 2005). In our experiments, depending on the input profiles, the effect is so large that nudging cannot prevent the fields from diverging without a very short nudging time scale ^{−2}) than that based on the adiabatic assumption and a ceilometer measurement of cloud base (~60 g m^{−2}). The larger LWP is mitigated by the shear-generated evaporation so that the LWP arrives at approximately the observed value at the end of the spinup run.

Through multiple tests we learned that 1)

For the current case,

The duration of the spinup run is 4 h. This might not be long enough for 25B (

The results of the spinup run for 6B are presented in Fig. 3. The other three spinup simulations (6H, 12B, 25B) show similar results to 6B. There is no notable systematic difference among results for the domain size and resolution tested. All of the ARW profiles are shown with a Tukey box plot for the last hour; the shadings are, however, not distinguishable owing to the narrow distribution of the first-moment quantities, suggesting that the fields are steady as a result of the nudging. The LWP settles down around the observed value (~60 g m^{−2}). The hourly mean model-derived cloud base (defined at the level of ^{−1}) compares well to the lidar estimate (Fig. 3b). Particular differences from the initial conditions are the weaker and more mixed

### b. Methodology for comparing ARW and lidar

The turbulence in the spinup run is in a quasi steady state due to the steady mean profiles, as expected (Fig. 3b). The lidar measurement over 1 h exhibits large temporal variability while ARW does not. This suggests that the comparison between spatial average (ARW) and temporal average along a line (lidar) requires special consideration.

At a given height, the lidar samples a two-dimensional line as it moves over the ocean surface (or the atmosphere advects over it). The model output is typically an average of the field over the entire domain for the sampling time in question. To address this disparity, we sample the model domain as if it were being viewed by the lidar. To do so we employ the Lagrangian Parcel Tracking Model (LPTM; YR12) within ARW to perform Lagrangian column tracking, which mimics the ship’s sampling of the atmosphere. LPTM places massless parcels (or particles) in the domain, then predicts each parcel trajectory using the spatially interpolated velocity from the host model’s resolved-scale velocity field, and performs the “measurement” with spatial interpolation. To represent the ship measurement, LPTM is modified so that each parcel travels with a fixed

The Lagrangian column tracking is performed from 0500 and 0900 UTC during the free run of 6B-2 (a variation on 6B discussed later). Four Lagrangian columns are arbitrarily placed inside the domain, and each column travels with the mean ship velocity [i.e., ^{−1}]. One column consists of 256 parcels, equally placed in the vertical below 1600 m. Velocity components are saved every second. During the 4-h period, each column travels 14.4 km. The spatial coverage based on the 4-h-mean wind (approximately −3.5 m s^{−1}) and the mean ship velocity is 36 km in the east–west direction, which is shorter than the spatial coverage based on the observed *u* owing to the deceleration of *u* during the free run (discussed later). Additionally, two other cases with different ship velocities [^{−1}] are performed. There is no significant difference among the three cases for the results discussed below.

The mean and variance profiles are derived in accord with the lidar measurements: 4-h-mean *u* and *υ* are removed as a background flow. The 4-h-mean *w* is set to zero. Profiles for mean and variance are then computed for every 10-min segment using the perturbation from the 4-h mean. Since lidar data are available for a period of 10 min, every 20 min, statistics for every other 10-min segment are discarded. Based on the profiles every 20 min, additional statistics are prepared with 40-, 60-, and 80-min means (i.e., averaging two, three, and four profiles).

The temporal variability for the different averaging time scales for one Lagrangian column with ARW’s spatial-mean profiles for 4 h is shown in Fig. 4. For the 10-min time scale, LPTM shows a wide temporal variability, much like the lidar observation, but that variability becomes narrower as the averaging time scale is increased. The variability in the 1-h mean of the LPTM and the variability in the horizontal mean of ARW over the 4-h period are similar in magnitude. Based on this exercise, the comparison for free runs will be performed with the 1-h mean of the lidar profiles (i.e., mean of three 10-min-mean profiles available every 20 min) and the spatial mean of ARW over the last 4 h of the simulation period.

### c. Adjustment for the free run

The time evolution of the LWP and inversion-top and -base heights for 6B with the original configuration is shown in Fig. 5a along with two additional cases (6B-1, 6B-2) listed in Table 1 and described below. Case 6B evolves in a way that the inversion-top and -base heights continuously elevate with a steady inversion thickness while the observed cloud-top height is somewhat steady. The LWP of 6B is approximately comparable to the observation. It should be noted that the shading for the LWP represents one standard deviation, computed at each given time; thus, there is significant spatial variability (Fig. 7). The relatively large observed LWP between 0400 and 0600 UTC exists in the model domain (e.g., Fig. 7b). The time series for ARW is calculated as a domain mean and therefore the smaller-scale variability that might be encountered by the ship along its narrow track is smoothed out.

Given the disparity between observed and modeled PBL height, in 6B-1 we applied increased large-scale divergence to alleviate the problem. After experimentation, *D* is relatively uncertain, it is quite possible that ARW overentrains by an amount influenced by the grid size and *D* as a tuning parameter.

Motivated by a desire to let the model compute surface forcing in an internally consistent way, 6B-2 is performed to investigate the effect of the interactive surface calculation, instead of specifying the friction velocity and surface fluxes. The computed surface forcing parameters are smaller than the observations (Fig. 5b). Interestingly, however, 6B-2 produces a smoother LWP time series, a steadier PBL height (Fig. 5a), a slightly stronger

The vertical profiles for 6B, 6B-1, and 6B-2 are shown in Fig. 6. For all cases *u* is weak compared with the lidar measurement, likely because of the absence of treatment of synoptic-scale flow such as the Chilean coastal low-level jet. A comparison between 6H (LES) and that with

The simulations all exhibit weaker turbulence than the observations. As expected from Fig. 5b, the turbulence for 6B-2 becomes more top-down oriented (i.e., radiatively driven). Overall, 6B-2 matches the observation better than 6B-1. The negatively skewed profile in *w* distribution compared to aircraft observations of northeastern Pacific stratocumulus. One can expect a similar smoothing influence of *w*. Since our

On balance, we concluded that the benefits of the interactive surface calculation outweigh the discrepancies between computed and observed values. For this reason, we adopt the modification made for 6B-2 (i.e., increased *D* and interactive surface calculation) for all free runs discussed below (sections 6 and 7).

## 6. Model comparison with observation for free runs

### a. Results of the free runs

A snapshot of LWP for 25B at the end of the free run (Fig. 7a) shows the appearance of several closed cellular circulations larger than a few kilometers in diameter. These cells are larger than the smaller domains tested. The normalized occurrence of LWP (Fig. 7b), created from the last 6 h of data saved every 10 min, emphasizes the effect of domain size and resolution on the LWP field. With increasing domain size (6B to 12B to 25B), there is a broadening in the distribution and an appearance of larger LWPs. This is also true for the finer resolution (i.e., 6B to 6H) and is at least partially due to an increase in the number of cloudy columns simulated, since the number of horizontal grid points is the same for 6H and 12B. For the larger domain, the broadening is probably related to the appearance of the near-mesoscale closed cellular circulation. The significant overlap between 12B and 25B indicates a tendency to convergence for the larger domains (at fixed resolution). Alternatively, the distribution may achieve convergence at higher resolution with a fixed *L*.

The time series of LWP and vertically integrated TKE,

The profiles for lidar comparison with the free runs are shown in Fig. 9. The *L*, the cloud-base height becomes lower and closer to the lidar estimate. As *L* increases, *w* statistics indicate stronger and more negatively skewed turbulence as the domain becomes larger, but the effect is not strong owing to the smoothing effect of *w* distribution (Guo et al. 2008). The temporal variation of the *w* statistics for 25B is much narrower than for the other cases over the last 4 h (Fig. 8b). This implies that the domain size is perhaps close to large enough so that the mesoscale cellular circulation is nearly free of constraint from surrounding cells.

### b. PSD analysis

Following DDJ04, we performed PSD analysis for modeled *u*, *υ*, *w*, and *u*, *υ*, and *w* and *u* are presented and discussed here. The PSD of the lidar-observed *w* is prepared as follows: To estimate the horizontal spatial scale of the variations in *w* during a single 10-min observation period, 1/2-s-resolution time series at each 30-m height bin were used to calculate the PSD as a function of height. An estimate of

The 4-h-mean PSD at selected levels for 6H and 25B are shown in Fig. 10a as a function of *w*, the PSD of the lidar data is also shown. The model spectra above the PBL (1500 and 1800 m) are one or two orders of magnitude smaller than those in the PBL. The shapes of the spectra are, however, similar at all levels. Since there is no turbulence in the free atmosphere, the power should have its source in the boundary layer turbulence—for example, via the upward transport of energy by gravity waves (Lilly 1983). For the small

An interesting feature is that for both *u* and *w*, 6B, 12B, and 25B (*w* spectrum, the low-resolution runs represent turbulence better than 6H for *u* and *w* for an adequately large domain size with the same resolution.

In Fig. 10 there is a notable difference in PSD shape between *w* and *u* at the larger *w* becomes weak for *u* continuously strengthens as *u*, the slope of the spectra for larger *w* and that the power weakens as *u*, *υ*, and *O*(10^{2} km) (Lilly and Petersen 1983; Nastrom and Gage 1985), and reproduced by the numerical weather forecasting mode of ARW for a domain of *O*(10^{3} km) (Skamarock 2004). We hypothesize that the absence of larger-scale motions greater than the domain size in the current simulations lacks an energy cascade from the larger scale, and that as a result a spectral peak appears for

Considering the above discussion and looking back at Fig. 10, as DDJ04 suggested, our largest domain (i.e.,

How large should the domain be for our case? Wood and Hartmann (2006) found that the characteristic scale of closed cells increases significantly when the PBL height is higher than 1 km; the characteristic scale jumps from 10 to 40 km as the PBL height changes from 760 to 1100 m. This implies that

Is the duration of our simulations long enough? The required duration of the simulation should scale with the size of the domain. The vertically averaged PSDs plotted every hour from 0500 UTC are shown in Fig. 10b. The power across all

For the lidar observations, the behavior of

## 7. Discussion

Generally, GASS LES intercomparison studies (Moeng et al. 1996; Bretherton et al. 1999b,a; Stevens et al. 2001; Brown et al. 2002; Siebesma et al. 2003; Duynkerke et al. 2004; S05; Ackerman et al. 2009; vanZanten et al. 2011; Blossey et al. 2013) show a wide spread of variability among participating models. Sensitivity of model results to various SGS and advection schemes are often discussed. Here, we perform three additional free runs based on 6B. One simulation is run without physical diffusion but with surface forcing. The other two simulations are run with second- and fourth-order momentum advection schemes.

The results for the run without physical diffusion and the run with the second-order momentum advection scheme are shown in Fig. 11. The shading of Fig. 11b covers the last 6 h for both model and observation, which is different to the time scale used in the previous section (4 h). The run with the fourth-order momentum advection scheme produces similar results to the run with the second-order scheme. The results are considerably different from those with the original configuration (6B). This is not a surprise since like the abovementioned GASS LES intercomparisons, these additional simulations are produced by models that differ from the originally configured ARW.

Turning off the physical diffusion produces larger LWP and stronger turbulence (S05) toward the end of the simulation, and provides a better match to the lidar measurement. Since the spatial scale for lidar (3–4 km) and the model domain size (

The second-order (and fourth order) momentum advection results in larger horizontal TKE than that of the original free run in the early stages when the LWP is similar. The even-order momentum advection preserves the shape of the turbulence profiles from the spinup run. The LWP decreases toward the end of simulation, as does the turbulence. This might be related to the buildup of energy at the shortest

## 8. Summary

Using a set of input measurements from the *RHB* during VOCALS-REx, we have examined the ability of the ARW to reproduce the turbulence profiles measured by NOAA’s high-resolution Doppler lidar. The influences of domain size (*L* = 6.4–25.6 km) and resolution are also examined.

A two-stage simulation strategy was developed to generate a realistic simulation in order to compare with the time-evolving observations. In the first “spinup” stage, the mean profiles are nudged to the observed profiles allowing the turbulence to develop and become steady. After some iteration and calibration of the initial soundings and

The simulated turbulence and observed turbulence are derived from two different averaging methods: the former uses a spatiotemporal mean, while the latter samples limited parts of the domain. A methodology is proposed to identify the appropriate spatiotemporal averaging scales for comparing these two different statistics. We utilize Lagrangian column tracking, which imitates the ship measurement inside the simulation domain. The analysis shows that depending on the averaging time scale, the temporal variability of the column statistics changes substantially. The temporal variation over 4 h between the spatial-mean ARW saved every minute and the 1-h-averaged Lagrangian column processed like the lidar measurements is comparable. Thus, with this averaging time scale, reasonable agreement would be expected if ARW were to reproduce the observed turbulence.

In the second, “free running” stage, we first modified our configuration so that a steady PBL top was maintained and the turbulence became more radiatively driven. These modifications result in turbulence closer to that observed, and better than the turbulence generated by the original free run, but the modeled turbulence is still underestimated. As *L* increases, the *w* turbulence shows weak sensitivity to these changes. A PSD analysis shows that the *L* until the spectral peak appears, while the *w* turbulence improves only slightly in response to the increased *L*. Once the spectral peak appears, the simulated turbulence improves very gradually when increasing resolution and *L*. Convergence is expected for both variables at sufficiently large *L*, provided that the resolution is fixed. Compared to the effect of *L*, the overall effect of resolution is minor for the resolutions tested. However, we found that the shape of the spectra differs with resolution, which may impose an artificial bias on turbulence and cloud water. Analysis of the effect of *L* and resolution on the variability of LWP suggests that it is expected to converge with sufficiently large domain and sufficiently high resolution.

Sensitivities associated with the model dynamics and physics are more significant than those associated with grid spacing and *L*. This fact sheds light on the ARW behavior for a prescribed configuration of the model dynamics and physics; for a given choice of core parameterizations (e.g., advection, diffusion), the model results are relatively insensitive to resolution and domain size. Much work remains to investigate the influence on ARW simulations of

This study is supported by the NOAA Climate Program Office through the Climate Process Team, Cloud Macrophysical Parameterization and its Application to Aerosol Indirect Effects (PI V. Larson). Useful discussion with the Climate Process Team is acknowledged. The authors would like to express their gratitude to the team on board the *RHB* for their efforts in acquiring such a valuable dataset. In particular, thanks are due to D. Covert for the aerosol size distribution data and P. Zuidema for the LWP data. The ECMWF operational data are courtesy of I. Sandu and M. Koehler.

# APPENDIX A

## Input Soundings and Data

The VOCALS-REx datasets are publicly available. Table A1 lists the data source and specific data used to construct input profiles as well as surface forcing.

List of data sources and data names.

The initial soundings for *u*, *υ*, *u*, *υ*, *u*, *υ*, and the number of samples at each level are used. Curve fitting and idealization are applied to obtain smooth profiles.

The

Observations of ^{−1} is specified for the free atmosphere. The mixed-layer and free-atmospheric profiles are connected with a linear fit. With these profiles, the cloud base is evaluated with a saturation adjustment. The value at the new cloud base is obtained by a linear fit with the same coefficient previously used for the subcloud-layer profile. The cloud-layer profile is reconstructed with the well-mixed assumption, and then the inversion profile (between

# APPENDIX B

## Acoustic Courant Number Convergence

YF12 evaluated the LES mode of ARW and found sensitivity of results to the acoustic Courant number [

For

# APPENDIX C

## Nudging

*t*is the time level, and the subscripts

*i*and

*j*(

*k*) represent the horizontal (vertical) components. We retain the horizontal indices for the following discussion, even though the above nudging term depends only on the vertical direction. As described in YF12, the horizontal mean profile is constructed with a vertical interpolation at a high-resolution height coordinate, which has 10 times the model vertical levels, owing to the fact that ARW is formulated with a mass vertical coordinate. The nudging tendency is, then, computed on each high-resolution level, and interpolated back to the local level.

*A*represents the advective tendency. By denoting(C3) can be written asQuick inspection of (C5) tells us that when

To achieve monotonicity after nudging for advection equation,

# APPENDIX D

## Computing Power Spectral Density

*k*, spectra, has the formwhere

*k*,

*L*is a length of space (or period),

*N*is a number of data points, and

*m*and

*n*are integers ranging

*n*is a discrete form of normalized

*k*. It should be noted that the unit of a spectrum is the unit of

*f*.

*s*:The advantage of using (D1) is that simple summation over all

*k*is equivalent to the total variance

*V*:

Frequently, only positive *k* values are used for the lateral axis. For this situation, in order to conserve *V*, one adds *n* becomes 0 and 0.5*N*.

*P*is useful, especially comparing data of different

*L*, because the area under the curve of PSD is

*V*so thatIt is straightforward to deduce that the PSD is given as

The unit of the PSD is the unit of *f*^{2} *k*^{−1}. One can show that (D5) is valid by starting with the continuous form of the spectral density obtained from the Fourier transform.

*p*and

*P*can be applied, so that

*k*are transformed to cylindrical coordinates

*k*, and

*V*can be expressed in continuous form asIn discrete form,

*V*in the cylindrical coordinate is expressed asso that PSD is given by

The two-dimensional power spectrum has two symmetry components. Before integrating *p* over the angle in (D11), *n* between 0 and 0.5*N* and the range of angles between

One can use various ways to integrate *p* over angles. Here we use *k*. In this way, the length of arc for all *k* is the same (i.e., *p* at every angle. The value of *p* for all *k* becomes less than 10^{−3}.

For zonal velocity, *p*(0) is much larger than that of *f* is used to compute *p* instead of the raw *f*.

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