Improved solar irradiance forecasts: modeling of shallow
cumulus clouds in the planetary boundary layer
Chang Ki Kim1,*, Michael Leuthold1, William Holmgren2, Alex Cronin2, Eric A.
Betterton1
1
Department of Atmospheric Sciences, University of Arizona, Tucson, Arizona
2
Department of Physics, University of Arizona, Tucson, Arizona
Submitted to Boundary-layer Meteorology
Corresponding Author:
Chang Ki Kim
Department of Atmospheric Sciences
University of Arizona
111 E 4th Street, Room 564
P.O.BOX 210081
Tucson, AZ, 85721-0081
ckkim@atmo.arizona.edu
Abstract
Accurate forecasts of solar irradiance are required for electric utilities to economically
integrate substantial amounts of solar power into their power generation portfolios. A common
failing of numerical weather models is the prediction of shallow cumulus clouds which are
generally difficult to be resolved due to complicated processes in the planetary boundary layer.
We improved turbulence parametrization for better predicting solar irradiance during the shallow
cumulus events by using the Weather Research and Forecasting model. Sensitivity tests show
that increasing the exchange coefficient leads to enhanced vertical mixing and a deeper mixed
layer. At the top of mixed layer, an adiabatically ascending air parcel achieved the water vapour
saturation and finally shallow cumulus is generated.
Key words
Solar irradiance, Shallow cumulus, Turbulence, Exchange coefficient, Weather Research and
Forecasting
1
1. Introduction
2
A major concern in solar power generation is the loss of incident solar irradiance due to
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passing clouds particularly in the case of photovotaics (PV). The effect of clouds on solar
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radiation has been of intense interest for several decades because of large variability (e.g.,
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Bishop and Rossow, 1991; Pfister et al., 2003). Sudden fluctuations of solar irradiance due
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to clouds can result in disruption to the electric grid and consequently can limit the
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adoption of solar power at the utility scale. To mitigate the economic losses, many
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irradiance and solar power forecasting systems have been developed (e.g., NREL, 2012;
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CREC, 2013). For short-term cloud forecasting (within a few hours), cloud cameras (e.g.,
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Chow et al., 2011), satellite imagery (e.g., Perez et al., 2004), and networks of irradiance
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sensors (Lonij et al., 2013) are often the most accurate techniques. Numerical weather
12
prediction with high resolution (NWP) remains the best tool for forecasting solar irradiance
13
from a few hours to days into the future and can also be used for daily forecasts of solar
14
power trading in the energy market. Therefore, NWP remains essential for the forecasting
15
of solar irradiance.
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The U.S., including Arizona, New Mexico and southeastern California is well known
17
as a good area for solar power generation yet despite the high annual irradiance, cloud
1
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systems make it difficult to integrate substantial amounts of solar power into utility grids. A
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major problem arises from the deep and moist convective systems during the summer
20
season, known as the North American monsoon (Adams and Comrie, 1997). The effects of
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heavy monsoon precipitation, such as floods that cause property damage or pose a threat to
22
life, have motivated the detailed study of cloud formation and precipitation in the region
23
(e.g. Balling and Brazel, 1987; Meitin et al., 1991; Dunn and Horel. 1994a, 1994b; Bright
24
and Mullen, 2002). In short, moisture supply from the Gulf of California and/or the Gulf of
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Mexico causes convective clouds with locally heated thermal during daytime in summer.
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In contrast to the moist convective clouds of the monsoon, there are few studies that
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attempt to better understand and predict shallow cumulus clouds because these clouds do
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not produce heavy precipitation. Even though the hydrometeorological impact of shallow
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cumulus is small, these clouds reduce solar power production by nearly as much as larger
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monsoon clouds (Benson et al., 1984). Shallow cumulus clouds over desert areas generally
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form due to the strong convection induced by the buoyancy flux and wind shear stress
32
during daytime. On a synoptic scale, the air within the planetary boundary layer (PBL) is
33
relatively drier in the pre- or post-monsoon than monsoon (Gamo, 1996; Bright and Mullen,
34
2002). To better predict shallow cumulus clouds, it is necessary for NWP to better simulate
2
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the turbulent mixing of heat and moisture in the PBL. Large eddy simulation (LES) reveals
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the best simulation of stratocumulus or shallow cumulus, the evolution of which is
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significantly dependent on the turbulent characteristics such as large eddy within PBL.
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Nevertheless, the computational burden of LES limits it to small domain case studies.
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Many three dimensional (3D) numerical models employ parametrization for turbulent
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processes within the PBL, and consequently the successful simulation of the shallow
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cumulus relies on how accurately turbulent transport of momentum, heat and moisture from
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the surface are predicted. As will be explained in detail later, for example, a comparison of
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PBL height between model and observation shows that the model predicts lower PBL
44
height than observation (Fig. 2c). A turbulence parametrization is examined thoroughly
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here because a determination of PBL depth is deeply related to the vertical mixing of
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momentum, heat and moisture by turbulence. In other words, it will be shown if increased
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exchange coefficient enhances the magnitude of turbulence and eventually PBL height can
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be raised to the altitude as high as shallow cumulus clouds from by the adiabatic cooling.
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The purpose of present study is to demonstrate that NWP is capable of accurately
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predicting shallow cumulus events over southeastern Arizona. To accomplish this goal, we
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first examine the seasonal trends of the PBL structure and thermodynamic structure in
3
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Section 2. Then, in Section 3, we describe four shallow cumulus case studies. Section 4
53
introduces our configuration of the Weather Research and Forecast model (WRF version
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3.5) (Skamarock et al., 2008) while sections 5 and 6 present and discuss the results of the
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sensitivity tests used to study how to better predict the shallow cumulus.
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2. Monthly variation of vertical thermodynamics
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Before examining the variation (30-days mean of the 0000 UTC observation) of the
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PBL structure, we introduce the observational data here for the period January 1 to
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December 31, 2013. Direct normal irradiance (DNI) is recorded every minute at the
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University of Arizona (http://www.nrel.gov/midc/ua_oasis). Sensible (SH) and latent (LH)
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heat fluxes, and friction velocity ( u* ) in the surface layer are measured at the Santa Rita
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Mesquite site, 48 km south of Tucson, as a part of the Ameriflux network (Scott et al.,
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2009). The vertical distribution of virtual potential temperature (θv) and wind speed (U) is
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obtained from the 0000 UTC (1700 local standard time, LST) rawinsonde launched at
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University of Arizona by the National Weather Service. The location of each observation
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site is illustrated in Fig. 1a.
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The PBL height is estimated from the elevation of the maximum gradient of θv in the
4
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upper portion of the PBL, as described in Fedorovich et al. (2004). Precipitable water and
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Convective Available Potential Energy (CAPE) are also derived from the rawinsonde.
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Monthly averaged cloud-top pressure and cloud fraction are obtained from the average over
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southern Arizona (marked in Fig. 3a) of the Moderate Resolution Imaging
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Spectroradiometer (MODIS) Level 3 cloud product aboard the Terra and Aqua satellites.
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Figure 2 shows the monthly variation of PBL height, cloud-top pressure, cloud fraction,
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precipitable water and CAPE. Cloud thickness is estimated here by taking the difference
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between the PBL height and cloud-top pressure. As expected, the thickest (convective)
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clouds were found in July while the shallowest clouds were found in September. The cloud
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fraction reaches a maximum in July, a minimum in October, and then increases again in the
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winter season. Clouds during the winter season are primarily driven by mesoscale dynamics
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such as fronts rather than the thermally induced convection because CAPE is negligible.
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Shallow cumulus often forms from March through June and in September because the PBL
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reaches a high altitude while cloud depth is relatively shallow due to the relatively weak
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CAPE.
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Estimation of the PBL height is a major concern in the modeling of shallow cumulus.
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This study compares the PBL height estimated from the rawinsonde with that modeled
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from the North American Regional Reanalysis (NARR). Figure 2c shows that the PBL
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height is underestimated by the models except in July when convective motion is strongest.
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The low bias of the PBL height produced by the NARR, although it is assimilated
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reanalysis, means that the PBL processes were not simulated reasonably in the first guess
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model. That is why the present study focuses on the turbulence parametrization to resolve
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the shallow cumulus modeling problem.
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3. Case description
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We selected four different cases for detailed analysis of shallow cumulus formation
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over Tucson, Arizona (Table 1) because shallow cumulus clouds are usually found for a
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few months and vertical structure of shallow cumulus for the cases used here shows the
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typical characteristics. These cases are classified into strong and weak shear-driven
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turbulence cases by daily mean of u* measured at Santa Rita Mesquite site; strong shear-
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driven turbulence case for daily mean of u* higher than 0.52 m s−1 but weak shear-driven
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turbulence case for daily mean of u* lower than 0.32 m s−1. The values used in
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classification are originated from Kim et al. (2003). The daily mean of u* for each case is
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given in Table 1. In the mixed layer, u* may be regarded as a measure of the turbulent
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kinetic energy (TKE) production by the surface wind shear stress (Stull, 1988). Mean sea
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level pressure at 0000 UTC is obtained from NARR. The Geostationary Operational
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Environmental Satellite-15 (GOES15) visible reflectance images are given for each case in
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Fig. 3. They all show that clouds exist over Tucson during the daytime and that a thermal
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low is generated in central Arizona. Figure 4 shows the vertical profiles of θv, U and bulk
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Richardson number (Rb) from the surface layer to each level calculated from the
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rawinsonde data. The mixed layer for all cases is fully developed into mid-levels by the
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positive buoyancy from surface heating during the daytime (Fig. 4a). U, however,
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represents the different characteristics between two groups: in weak shear-driven
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turbulence cases, the wind shear between the surface layer and upper level is much lower in
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magnitude. In addition, it is also true for Rb to be negatively smaller in weak shear-driven
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turbulence cases than in strong shear-driven turbulence cases because the contribution of
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wind shear stress to TKE is so small as to be negligible in weak shear-driven turbulence
116
cases (Fig. 4c). Therefore the mixed layer is as a result of the wind shear stress and
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buoyancy flux from the surface layer in the strong shear-driven turbulence cases, while the
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buoyancy flux dominates the vertical growth of PBL in weak shear-driven turbulence cases.
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The time series of DNI reveals the effects of shallow cumulus clouds on the solar
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irradiance measured at the ground (Fig. 5). Rapid fluctuations of DNI are frequently
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observed in the afternoon because shallow cumulus obscures the incident solar energy. The
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high temporal variability of the DNI is indicative of the small size of the shallow cumulus
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clouds.
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4. WRF Configuration
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4.1 PBL parametrization
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As stated in the introduction, most 3D mesoscale models parametrize the turbulent
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transport of momentum, heat and moisture. We used the Medium-Range Forecast (MRF)
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scheme (Hong and PAN, 1996) because Bright and Mullen (2002) showed that it correctly
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predicts the development of a deep and moist PBL and consequently does a better job of
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predicting CAPE, compared to the other PBL schemes. We note that this scheme has
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already been updated into the Yonsei University (YSU) scheme (Hong et al., 2006).
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The heat and moisture fluxes are computed using a modified K theory in the MRF
scheme, so that the flux of any arbitrary variable (C) is represented by
C    C

 K c 
  c  ,
t z   z

(1)
where γc is a countergradient term. The addition of γc to Eq. (1) allows for countergradient
8
137
fluxes to be represented by the parametrization as non-local mixing. Hong and Pan
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(1996) defined the exchange coefficient for momentum (Kzm) to be
p
139
K zm
z

 kws z 1   ,
 h
(2)
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where k is the von Kármán constant (assumed to be 0.4), ws is the mixed-layer velocity
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scale, z is the height above ground, h is the PBL height, and p is assumed to be 2.0. The
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transfer coefficient for heat (and similarly for moisture) is related to Kzm by the Prandtl
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number.
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The exponent p in Eq. (2) is a crucial factor in determining the magnitude of the
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exchange coefficient for momentum, with smaller values leading to stronger vertical
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mixing, and in determining the level at which the exchange coefficient is a maximum as
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well. Nielsen-Gammon et al. (2010) suggests that the plausible range of p is from 1 to 3.
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Hu et al. (2010) showed that the PBL height rose to higher altitudes in the simulation with
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smaller values of p. Vertical profiles of normalized Kzm computed for a range of p values
150
are shown in Fig. 6. As the value of p decreases, the magnitude of Kzm increases, and the
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altitude at which the Kzm becomes a maximum also increases.
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4.2 Numerical experiment setup
9
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Figure 1b shows the domain setting for the WRF simulations, where a one-way grid
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nesting procedure was employed for the two domains. The grid spacing of the outer and
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inner domains is 5.4 km and 1.8 km, respectively. The outer domain has 460 by 430 grid
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cells and 44 vertical layers with the top level at 100 hPa. The outer domain is nested into
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the inner domain which has 430 by 352 grid cells. The three-hourly data from the North
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American Mesoscale Forecasting System (NAM) produced by the National Oceanic and
160
Atmospheric Administration (NOAA) are used as the initial and boundary meteorological
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conditions for the WRF simulations. The selected set of physical parametrizations is
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RRTMG (Mlawer et al., 1997) for shortwave and longwave radiation, the Morrison 2-
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Moment scheme for microphysics (Morrison et al., 2009), the MM5 scheme (Paulson, 1970)
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for the surface layer, and NOAH LSM (Chen and Dudhia, 2001) for the land-surface model.
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The MRF scheme is used here for PBL processes but it is modified for our sensitivity tests.
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The sensitivity of convective parametrization to the redistribution of heat and moisture was
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so small as to be ignored here (not shown).
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Table 2 summarizes the four simulations described here. The BASE simulation uses
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the original MRF scheme for the PBL process. The MRFE simulation is the same as the
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BASE simulation except that p is reduced from 2.0 to 1.0 in Eq. (2), as explained in
10
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subsection 4.1. A comparison between the MRFE and MRF0 simulations show how the
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critical Richardson number (Rc) influences the estimation of PBL height. In addition, the
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YSU simulation is designed to see the influence of the exponent, p on the determination of
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Kzm in Eq. (2). Each simulation was done for 24 hours starting at 1200 UTC (Table 1). The
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results discussed below come from the model output for the inner domain, which is
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produced every 3 minutes, and the vertical profiles corresponding to each observation site.
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5.
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5.1 BASE simulation
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A comparison between observations and the BASE simulation forecasts is useful for
181
evaluating the original MRF scheme to predict the vertical structure of the thermodynamics.
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Figure 7 shows the vertical profiles of θv from the 12-hour forecast, corresponding to 0000
183
UTC for each day, and the corresponding observation at 0000 UTC. In both of the strong
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shear-driven turbulence cases, the BASE simulation shows a lower PBL height than the
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observation and a cold bias in θv in the mixed layer (Fig. 7a and 7b). A stable layer exists
186
above the mixed layer in the BASE simulation but observation shows a strong capping
187
inversion above the mixed layer. The simulated lower PBL height makes it difficult for an
Results
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air parcel ascending adiabatically to achieve water vapour saturation and for clouds to form.
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The DNI predictions shown in Figure 5a and 5b confirm that clouds do not form during the
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afternoon in the BASE simulation. Contrary to the strong shear-driven turbulence cases, the
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BASE simulation done for weak shear-driven turbulence cases successfully predicts the
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vertical thermodynamic structure including the PBL height and θv in the mixed layer (Fig.
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7c and 7d). In addition, the capping inversion for weak shear-driven turbulence cases is
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well defined in the BASE simulation. Figures 5c and 5d show that DNI is reduced in the
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afternoon in weak shear-driven turbulence cases due to shallow cumulus. The discrepancy
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of the PBL structure between the strong and weak shear-driven turbulence cases will be
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discussed in Section 6.
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5.2 Sensitivity simulations
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Three additional simulations for each strong shear-driven turbulence case were run to
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better diagnose the PBL structure. MRFE shows the best performance in generating a deep
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mixed layer in both strong shear-driven turbulence cases, although the PBL height is still
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lower than the observation by 200 m, with enhanced vertical mixing by reducing the
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exponent, p in Eq. (2) (Fig. 7a and 7b) because increased turbulence can overshoot the
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inversion layer above and then mixed layer can be deepened. The MRF0 simulation used
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the same value of p as MRFE but Rc was reduced from 0.5 to 0. The PBL height in MRF0
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is lower than the MRFE simulation in both of the strong shear-driven turbulence cases.
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Even in the second strong shear-driven turbulence (ST2) case, the MRF0 simulation
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predicts a mixed-layer depth similar to that in the BASE simulation. A value of Rc > 0
210
represents a contribution of wind shear stress to the TKE under conditions where the
211
buoyancy flux is negative. Consequently, reducing Rc to 0 does not allow PBL height in the
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turbulence parametrization to be raised only by the wind shear stress without buoyancy.
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This is consistent with the major findings of Hong et al. (2006). The YSU simulation shows
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a lower PBL height than MRF0 in both strong shear-driven turbulence cases. Although the
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YSU scheme uses the same Rc as that in MRF0, the enhanced vertical mixing in MRF0
216
plays a more significant role in deepening the mixed layer.
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In spite of the remarkable improvement of PBL simulations in the MRFE simulation,
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the reduction of DNI caused by the shallow cumulus in the afternoon is only seen in the
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ST2 case. Failure to form shallow cumulus in the MRFE simulation for the first strong
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shear-driven turbulence (ST1) case may be related to the humidity in the mixed layer. The
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mean water vapour mixing ratio (qv) at 0000 UTC on March 23 in the mixed layer was 2.7
13
222
g kg−1 (observed) and 2.1 g kg−1 (MRFE), respectively. The dry bias within the PBL in the
223
MRFE simulation results in a cold bias in θv as shown in Fig. 7a. Figure 5b shows that DNI
224
is nearly zero after 2100 UTC on September 26 in the MRFE simulation while the observed
225
DNI undergoes a large fluctuation. This may be due to the inherent problem of comparison
226
at a single point (Gibbs et al., 2011). In the grid system, model data for a single grid cell
227
represents the local atmospheric state as a statistical mean over the entire cell whereas the
228
measured data is obtained at a single point arbitrarily located with respect to the model grid
229
cell. Another way to explain the difference of DNI between the observation and the model
230
output is that the areal extent of simulated clouds is somewhat broader. This issue will be
231
discussed shortly in the Section 6.
232
Meanwhile, the time-height plot in Figure 8 shows the formation of shallow cumulus
233
after modifying the MRF scheme. The top of PBL is lifted to 4200 m in the MRFE
234
simulation (Fig. 8b), showing that an air parcel ascends wet-adiabatically with CAPE. As a
235
result, the cloud water mixing ratio in the MRFE simulation is higher than in the BASE
236
simulation.
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6.
Discussion
14
239
In the previous section, we found that a large discrepancy in the PBL height exists
240
between the strong and weak shear-driven turbulence cases. The selected cases were
241
originally classified by the magnitude of wind shear stress and therefore we focus on the
242
contribution of wind shear stress to the TKE derived from the rawinsonde data and the
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model output at 0000 UTC for two cases, as shown in Fig. 9. The observed wind shear
244
stress in strong shear-driven turbulence cases is higher in magnitude than that in the weak
245
shear-driven turbulence cases. This makes sense because the mechanically induced
246
turbulence is significantly related to the high wind speed and friction velocity (Stull, 1988).
247
Although the evolution of PBL depth is dominated by the wind shear stress and positive
248
buoyancy flux in cases of strong shear-driven turbulence, the magnitude of the modeled
249
wind shear stress in the BASE simulations is lower than observed. This means that the
250
modeled PBL height in the BASE simulations could be lower than the observation because
251
of the weak contribution of wind shear stress to the generation of TKE. The wind shear
252
stress itself for weak shear-driven turbulence cases, as shown in Fig. 9b, is also predicted to
253
be lower than the observed value but the impact of wind shear stress on producing TKE in
254
these cases is much smaller than in strong shear-driven turbulence cases (see Fig. 4c). We
255
can say tentatively that wind shear stress has little effort in determining the TKE and PBL
15
256
height, at least for the weak shear-driven turbulence cases here. Consequently, the WRF
257
model used here shows better performance in weak shear-driven turbulence case than
258
strong shear-driven turbulence case.
259
We now consider the influence of surface heat fluxes on the magnitude of Kzm.
260
Because surface heat fluxes are deeply related to ws in Eq. (2) as the source of TKE, the SH
261
and LH, measured at the Santa Rita Mesquite site (Fig. 1a), are compared to the modeled
262
output as a function of time in order to examine how the model represents the surface heat
263
flux (Fig. 10). With the original MRF scheme, the behaviour of SH and LH is entirely
264
consistent with the observed surface heat fluxes in phase and magnitude for the case of ST1
265
(Fig. 10a). At 1900 UTC (local noon), predicted SH exceeds the observation, which means
266
that more energy is transported from the surface into the PBL by large eddies in the model.
267
Figure 10b shows that the model produces higher LH than observed in the ST2 case. Rabin
268
and Martin (1996), and Golaz et al. (2001) show that a higher LH leads to a shallower PBL
269
depth and a lower cloud base height. In other words, the evapotranspiration from the
270
canopy and wet soil moisture plays a role in lowering the lifted condensation level and
271
thickening the cloud depth. The predicted SH at local noon is still stronger than observed
272
(Fig. 10b), however. Therefore, the lower PBL height seen in the BASE simulation implies
16
273
that there is difficulty in transporting the momentum, heat and moisture from the surface
274
layer to the upper level, although the higher SH could be a source of TKE.
275
We now increase Kzm in Eq. (2) by reducing the exponent p from 2.0 to 1.0 to enhance
276
the magnitude of vertical mixing of momentum, heat and moisture between two adjacent
277
layers. The vertical profiles of Kzm from the BASE and MRFE simulations for the strong
278
shear-driven turbulence cases are shown in Fig. 11. It is not surprising that Kzm increases
279
and the vertical level at which the Kzm is the highest is found at higher altitude in the MRFE
280
in both strong shear-driven turbulence cases. To examine the effect of increased Kzm on
281
turbulence, we compare the vertical profile of Rb as a function of time in the BASE and
282
MRFE simulations (Fig. 12). Within the PBL in both of the BASE and MRFE simulations,
283
negative Rb suggests that the production of TKE is dominated by buoyancy flux and wind
284
shear stress. However, the area showing negative Rb is stretched into higher levels in the
285
MRFE simulation than in the BASE simulation. The magnitude of Rb is reduced in the
286
MRFE simulation, implying that the wind shear stress is increased by the transported
287
momentum from the surface layer in enhanced large eddies.
288
For solar energy forecasting, it is of interest to understand the horizontal distribution
289
of shallow cumulus clouds. When the boundary layer is heated by the surface, instability
17
290
may arise and then convective overturning may occur in the form of long rolls or
291
symmetric cells, i.e., cloud streets (Houze, 1993). Figure 13 compares satellite imagery
292
(GOES15, 11 μm) with the model output. Cloud streets are seen over southern Arizona,
293
including Tucson, in Fig. 13a. The BASE simulation does not show clouds over Tucson but
294
cloud streets are simulated in MRFE (Fig. 13b and 13c). Nevertheless, the predicted
295
horizontal extent of the clouds over Tucson is more widespread in the MRFE simulation
296
than is actually observed. Consequently the predicted DNI patterns seen in Fig. 5b do not
297
have the temporal fluctuations observed at the ground due to widespread clouds.
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299
7.
Conclusion
300
The present study examines the performance of WRF-modeled shallow cumulus clouds
301
during pre- and post-monsoon seasons in the southwest U.S to improve the prediction of
302
solar power generation. Deep, moist convective clouds are generally formed during the
303
North American Monsoon but shallow clouds are occasionally generated by the strong
304
surface heating during pre- and post-monsoon seasons. As is seen by the analysis of vertical
305
profiles at the University of Arizona, the PBL height is lifted to higher altitudes during
306
daytime as a result of dry convection during the pre- and post-monsoon seasons. The
18
307
estimated PBL depth from NARR is shallower than observed, implying that there is
308
problem in simulating the deep mixed layer. Hence, this study attempted to identify why
309
the model predicts a shallow PBL and then to resolve the modeling problems. To
310
accomplish the major goal of this study, we performed sensitivity tests for four different
311
cases, two of which exhibit strong shear-driven turbulence in the mixed layer. Based on the
312
work of Bright and Mullen (2002), the MRF scheme for PBL processes was employed as a
313
reference scheme and then modified in the sensitivity tests. This makes sense because the
314
turbulent processes are more highly relevant to the formation of shallow clouds than other
315
forcings such as synoptic flow.
316
As a result of the BASE simulation, the model performance is found to be better in the
317
weak shear-driven turbulence cases than in the strong shear-driven turbulence cases. That is
318
because the WRF model with the MRF scheme for strong shear-driven turbulence cases
319
tends to produce wind shear stresses that are weaker than observed. A comparison of
320
surface heat fluxes at the surface layer between the model and observation drives the model
321
in the right direction: increasing the exchange coefficient in the WRF model transports the
322
momentum, heat and moisture to higher levels. As the turbulence gets stronger within the
323
PBL, the mixed layer is deepened and consequently adiabatically ascending air parcels
19
324
attain water vapour saturation. The shallow cumulus formed by the enhanced vertical
325
mixing reduces the DNI. Satellite imagery showed cloud streets over southern Arizona but
326
the simulated clouds covered a broader areal extent than observed. This will be further
327
studied in the future. The life time of either shallow or small cumulus is dominated by the
328
cloud microphysics, including cloud condensation nuclei (CCN) as well as turbulence in
329
the PBL (Lee et al., 2008). A study of the relationship between clouds and aerosols in the
330
southwest would provide further insights into the influence of shallow cumulus on DNI.
331
Twomey (1977) showed that increased concentrations of atmospheric aerosol will result in
332
higher concentrations of CCN, increased cloud droplet concentrations, and furthermore
333
Albrecht (1989) suggested that smaller droplets and increasing the number of CCN
334
suppresses precipitation and results in more reflective clouds both because droplets are
335
smaller, and because a larger liquid water path is maintained. Therefore more sophisticated
336
microphysics which could estimate important radiative characteristics such as cloud droplet
337
effective radius would contribute to better solar forecasting.
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340
Acknowledgements
This work was funded by Tucson Electric Power (TEP). The authors would like to
20
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express deep thanks to Dr. Russell L. Scott for providing micrometeorological data from
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the Santa Rita Mesquite Site.
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References
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442
26
443
444
Table 1. Summary of selected cases, classified by the daily average of friction velocity
445
u* , (± standard deviation) measured at a location of Santa Rita Mesquite, AZ station.
Case
Shear Stress
Simulation period (UTC)
u* (m s−1)
ST1
Strong
2013-03-22 1200 ~ 2013-03-23 1200
0.60±0.19
ST2
Strong
2013-09-26 1200 ~ 2013-09-26 1200
0.63±0.29
WT1
Weak
2013-06-16 1200 ~ 2013-06-17 1200
0. 30±0.15
WT2
Weak
2013-09-18 1200 ~ 2013-09-19 1200
0.23±0.08
446
447
448
449
450
451
452
453
454
27
455
456
Table 2. Summary of simulations performed in this study. The exchange coefficient
457
(Kzm) is calculated using Eq. (2) in the text and the critical Richardson number (Rc) is
458
given.
z

 kws z 1  
 h
p
Experiment
PBL
BASE
MRF
p=2.0
0.5
MRFE
MRF
p=1.0
0.5
MRF0
MRF
p =1.0
0.0
YSU
YSU
p=2.0
0.0
K zm
Rc
459
460
461
462
463
464
465
466
28
Remark
Grid resolved entrainment
467
(b)
(a)
468
469
Figure 1. (a) Map of southern Arizona and (b) WRF domains. Triangle, closed circle
470
and asterisk indicate the locations of the University of Arizona, Tucson International
471
Airport and Santa Rita Mesquite site, respectively.
472
473
474
475
476
477
478
479
480
29
481
0.8
600
0.6
700
0.4
800
0.2
900
Precipitable Water (mm)
1000
50
40
0.0
1000
(b)
800
30
600
20
400
10
200
PBL height (m)
0
6000
5000
CAPE (J kg-1)
Pressure (hPa)
500
1.0
(a)
Cloud Fraction
400
0
(c)
4000
3000
2000
1000
0
Jan
Feb
Mar
Apr
482
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Month
483
Figure 2. (a) Monthly distribution of the Planetary Boundary Layer (PBL) pressure
484
(solid line with diamond), cloud top pressure (dashed line with rectangle) and cloud
485
fraction (blue dashed line with triangle); (b) precipitable water (solid line) and
486
convective available potential energy (vertical bar); and (c) PBL height from the
487
rawinsonde (solid line with circle) and North American Regional Reanalysis (dashed
488
line with rectangle) at Tucson.
489
30
490
(a)
(b)
(c)
(d)
491
492
Figure 3. (a) Visible satellite image (shaded area) and mean sea level pressure (contour
493
line) at 0000 UTC of March 23, 2013; (b) September 27, 2013; (c) June 17, 2013; and
494
(d) September 19, 2013. The black box in each figure indicates the city of Tucson,
495
Arizona. Contour minimum and interval are 980 hPa and 4 hPa, respectively.
496
31
497
5000
Height (m)
4000
3000
2000
1000
(a)
0
300
498
305
310
315
v 
320
325
(c)
(b)
0
5
10
15
20
-1
WS (m s )
25
30 -5.0
-2.5
0.0
2.5
5.0
Rb
499
Figure 4. Vertical profiles of (a) virtual potential temperature; (b) wind speed; and (c)
500
bulk Richardson number (c) at 0000 UTC. In each plot, black solid, black dashed, red
501
solid and red dashed line indicate the ST1, ST2, WT1 and WT2. Case studies of ST1,
502
ST2, WT1 and WT2 are summarized in Table 1.
503
504
505
506
507
508
32
509
1200
(a)
(b)
(c)
(d)
1000
DNI (W m-2)
800
600
400
200
0
1200
1000
DNI (W m-2)
800
600
400
200
0
12
510
13
14
15
16
17
18
19
20
21
22
23
0
1
2
Time (UTC)
3 12
13
14
15
16
17
18
19
20
21
22
23
0
1
2
3
Time (UTC)
511
Figure 5. Time series of direct normal irradiance measured at the University of
512
Arizona (black line) compared to forecasts from BASE (red line), MRFE (blue line),
513
MRF0 (green line) and YSU (gray line) for (a) ST1; (b) ST2; (c) WT1; and (d) WT2
514
(d). BASE, MREF, MRF0 and YSU are summarized in Table 2.
515
516
517
518
519
33
520
Height above ground level (m)
2000
0
50
100
150
200
250
300
350
400
1500
1000
500
0
3.0
521
2.5
2.0
1.5
1.0
p
522
Figure 6. The vertical profiles of normalized exchange coefficient for momentum (Kzm)
523
as a function of p, the exponent in Eq. (2) used to calculate Kzm. The height of
524
planetary boundary layer is set as 2000 m.
525
526
34
527
Height above ground level (m)
5000
4000
3000
2000
1000
(a)
(b)
Height above ground level (m)
0
5000
4000
3000
2000
1000
(c)
(d)
0
300
305
310
315
v (K)
320
325 300
305
310
315
320
325
v (K)
528
529
Figure 7. Vertical profiles of virtual potential temperature derived from the
530
rawinsonde launched at the University of Arizona at 0000 UTC for each case,
531
compared to forecasts from BASE (red line), MRFE (blue line), MRF0 (green line)
532
and YSU (gray line) for (a) ST1; (b) ST2; (c) WT1; and (d) WT2.
533
35
534
(a)
(b)
535
536
Figure 8. Time-height plot of relative humidity (contour line) and cloud water mixing
537
ratio (shaded area) from (a) the BASE and (b) the MRFE for the ST2 case at a grid
538
cell corresponding to the location of Tucson. Contour minimum and interval are 50%
539
and 10%, respectively.
36
540
Height above ground level (m)
5000
4000
3000
2000
1000
(a)
(b)
0
0.0
541
0.2
0.4
0.6
0.8
1.0 0.0
0.2
0.4
0.6
0.8
1.0
-4
2 -2
Wind Shear stress (x10-4, m2 s-2) Wind Shear stress (x10 , m s )
542
Figure 9. Vertical profiles of wind shear stress derived from the rawindsonde at
543
University of Arizona (solid line) and the BASE simulation (dashed line) for (a) the
544
ST1 (no symbol) and ST2 (circle); and (b) the WT1 (no symbol) and WT2 (circle) at
545
0000 UTC.
546
547
548
549
37
550
500
(a)
Surface Heat Flux (W m-2)
400
Sensible Heat
300
200
100
0
Latent Heat
-100
500
(b)
Surface Heat Flux (W m-2)
400
Sensible Heat
300
200
100
Latent Heat
0
-100
13
16
19
22
0
3
6
Time (UTC)
551
552
Figure 10. Time series of surface heat fluxes derived from observation, made at the
553
Santa Rita Mesquite site (solid line) and the BASE simulation (dashed line) for (a) ST1;
554
and (b) ST2.
38
555
Height above ground level (m)
5000
4000
3000
2000
1000
(a)
(b)
0
0
556
100
200
300
400
500
600
700 0
Kzm (m2 s-1)
100
200
300
400
2
500
600
700
-1
Kzm (m s )
557
Figure 11. The vertical profiles of exchange coefficient for momentum from the BASE
558
(red) and MRFE (blue) for the (a) ST1; and (b) ST2 at a grid cell corresponding to the
559
location of Tucson at 0000 UTC for each case.
560
561
562
563
564
565
566
567
568
39
569
(a)
(b)
(c)
(d)
570
571
Figure 12. Time-height plot of bulk Richardson number from (a) the BASE; and (b)
572
the MRFE for the ST1; and from (c) the BASE; and (d) the MRFE for the ST2 at grid
573
cell corresponding to the location of Tucson.
574
575
576
577
578
579
580
581
40
582
(a)
(b)
(c)
583
584
Figure 13. Brightness temperature (11 m) from (a) the satellite; (b) the BASE
585
simulation; and (c) the MRFE simulation at 0000 UTC, September 27, 2013 (ST2 case).
586
41