Analysis of Surface Flux Impacts on Low Level Stratoform Cloud Ceilings Final ProjectDavid R. Lewis
: OC 3570
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I. Introduction and Background:
During the course of the OC3570 cruise from 24‐29 July 2009, the area
around San Nicholas Basin in which we operated was under the influence of a
capping inversion. This capping inversion was typical of the climatology of this
region in the summertime but was unusually persistent throughout the duration of
our cruise. Winds were consistently light (0‐10 m/s) and westerly (mean of 275
degrees), again, typical of the climatology. As a result, a unique opportunity was
presented to us to examine relationships between the air‐ocean interface and cloud
ceiling bottoms, somewhat independent of advective processes. Analysis of air‐sea
interaction relationship to atmospheric weather could give important insights into
the physics of cloud formation, and could provide the Department of Defense (DoD),
and the meteorology community as whole, with the information required to develop
improved methods of parameterization in modeling. Therefore, the purpose of this
study is to calculate and compare various fluxes associated with the air‐ocean
boundary layer to determine the nature of the influence these fluxes may have on
ceiling bottoms.
In 2008, Erick Edwards examined sensible and latent heat fluxes, as well as
wind stress, in an attempt to find correlation with the mixed layer depth, but did not
calculate buoyancy fluxes due to lack of evaporation and precipitation data.
Edwards verified that a positive correlation existed between wind stress and the
sensible and latent heat fluxes. He also observed a 2 to 1 ratio between latent and
sensible heat flux on the Winter 2008 cruise along the central California coast. Chu
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and Garwood (1990) proposed a one‐dimensional thermodynamic feedback loop
between precipitating cloud formation and the ocean mixed layer, and implicitly to
heat and buoyancy fluxes. While their primary conclusions were oriented towards
significant weather development in the tropics and the growth of precipitating
clouds, elements of the theory might be applicable to our generally stable
environment.
I surements and Data ManipulationI. Mea :
During the period 24‐29 July, over 28000 measurements of meteorological
parameters were made at 15 second intervals. These parameters included air
temperature, Relative Humidity (RH), wind speed and direction, as well as longwave
and shortwave radiation. Air temperature and relative humidity were measured by
a Rotronic model MP100H combined probe with a separate temperature probe
(Pt100 1/10 DIN). The temperature probe was housed in a naturally ventilated R.
M. Young model 41003 multi‐plate radiation shield and had an attached HygroClip
S3 used for the RH measurements. The measurement error is within ±1.5% for RH
and ±0.2°C for temperature (at 23°C / 73°F). Relative wind speed and direction
were measured via the R. M. Young model 05103 wind monitor with an accuracy of
±0.3 m/s (0.6 mph) or 1% of reading for wind speed, and ±3 degrees for wind
direction. The long‐wave radiation measurements were made via an Eppley
Laboratories Precision Infrared Radiometer (PIR). This sensor measures in the 3.5‐
50 micrometer wavelength band with a 180 deg field of view and has a sensitivity of
pproa ximately 4 µV/Wm-2.
Measurements of ceiling heights were collected by a ship mounted Vaisala
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Model CT25K ceilometer, which infers ceiling height by a measurement of the
optical backscatter intensity of the air at a wavelength of 905 nm. Ceilometer
measurements had a spatial resolution of 15 meters from the ground up to an
altitude of 7500 meters.
All of this sensor data was fed into a Campbell Scientific Model CR1000
measurement and control data‐logger for collection and internal processing.
Corrections for true wind speed and direction were done with inputs from a
compass and GPS. The correction software is built into the logger routine and
includes an in‐situ correction to the compass using GPS heading when the vessel is
moving at more than 2 m/s. This ensured more accurate true directional readings.
In addition, radiometer data corrections for internal temperature (casing and
hemisphere) were incorporated into the CR1000 coding.
Much of the data collected by the CR1000 suite was converted by the NPS
faculty into a .mat variable file, which could be used in MATLAB to perform more
specific calculations. Dr. Guest provided the MATLAB code to calculate wind stress,
and sensible and latent heat fluxes from the other meteorological variables. Since
the code was designed to provide a single point calculation, it had to be modified
slightly to calculate fluxes across an entire time‐series. Richard Lind provided raw
ceilometer data, averaged down from 15‐second increments to 1‐minute intervals.
This data had to be converted into MATLAB vector format. To ensure continuity in
comparison, several adjustments to the data were then made. All non‐
number/invalid values from any data vector had to be removed. In addition, there
were several periods where Relative Humidity was recorded as 120%. This data
was adjusted to 100%. After these corrections, all the corresponding data sets had
to be filtered so that their time steps were exactly matched and the vector lengths
equal.
Next, the meteorological data had to be interpolated onto the ceilometer
time‐series vector to allow for common comparison between all parameters. A
standard linear interpolation was used for this process. Linear interpolations
generally create more error compared to other interpolation methods, but in this
case, error would be minimal since the ceilometer data points are an exact match to
every fourth data point for the other meteorological data. Finally, all data points
registered as ‐9999 on the ceilometer data vector were purged. These represented
points in time where a ceiling did not exist. Corresponding data points on the other
data vectors were also removed.
III. Analysis:
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ig. 1: Ceiling Heights plotted over New Horizon’s route, 24‐29 July, 2009.
Figure [1] gives us an overview of the ceilometer data collected over the
course of the summer 2009 cruise. Correlations between these heights and
interface fluxes are predicated on one major assumption: that the time series data is
treated as if it was obtained from one location. This assumption can be made if we
observe three facts:
1.) Atmospheric horizontal advective processes are not sufficient to change
the overall vertical structure of the atmosphere. This was true
throughout most of our cruise.
2.) Flux measurements are more dependent upon static properties (such as
relative humidity (RH), pressure, density, etc.) Therefore, we are not
concerned with a time or spatial change of one of these parameters
affecting ceiling height at one point in time and space. Instead we are
merely comparing ceiling height at a single point with atmospheric state
at that same point.
3.) Fluxes act primarily in the vertical axis. While horizontal winds and
currents affect the flux output, the output is still vertically oriented.
Displaying these profiles on a single time‐series gives us some insight into the
overall ceiling‐flux relationships.
Figure [2] gives us this representation for ceiling bottom heights, while figure
[3] displays sensible and latent heat fluxes along with the air temperature‐sea
urface temperature (SST) difference on a GMT time‐series.
]: Time‐series representation of ceiling bottom heights. Values are computed using a running average size of 60. Note: Times/dates are GMT.
Figure [2with a window
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Figure [3]: Time‐series representations of air temperature‐SST difference along with sensible and latent heat fluxes. Note: Times/dates are GMT; Actual values for LHF and SHF are negative, but shown here as a positive into the atmosphere.
Sensible and latent heat fluxes are computed according to the following
equations:
Sensible Heat Flux (SHF): (1) Where:
) Qsen = Sensible Heat Flux (W/m2 ρa = Air Density (kg/m3) CH = Transfer Coefficient Ta = Air Temperature (ºC)
cpa = Specific Heat of Air (J/kg ºC) S = Relative Wind Speed (m/s) Ts = Sea Surface Temperature (ºC)
Latent Heat Flux (LHF): (2) Where:
a Qlat = Latent Heat Flux (W/m2) ρ = Air Density (kg/m3) CE = Transfer Coefficient qa = Specific Humidity (g/kg)
L = Latent Heat of Evaporation (m2/s2) S = Relative Wind Speed (m/s) qs = Saturated Specific Humidity (g/kg)
Note that negative values represent positive heat flux into the atmosphere. From
figures 2 and 3 we see that both air and sea surface temperatures generally follow
diurnal patterns of heating and cooling, as do the latent heat flux values and ceiling
bottom heights. Sensible heat flux does not follow this diurnal pattern as drastically
as the other three parameters. We also note that SST is higher than the air
temperature throughout the cruise, confirming our belief that heat flux should be
irected d into the atmosphere.
Using the cruise values for the above heat fluxes, as well as cruise derived
values for precipitation, short and long wave radiation, and evaporation, we can
ompute the Buoyancy Flux: c
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(3)
Where : (4)
ent B Buoyancy Flux (m2/s3) β = Salinity Contraction Coefficiw
0 = = Thermal Expansion Coefficient α ρ = Water Density (kg/m3)
cρ(w)=Specific Heat of water (J/kg . oC) E = Surface Evaporation (m/s) Pr=Precipitation Rate (m/s) Ss = Near Surface Salinity (g/kg)
2) W)
g = Gravity (m/s2) Fτ= Net Surface Heat Flux (W/mRb=Long‐wave Radiation Loss (W) Rs=Short‐wave Radiation Gain(L=Latent Heat of Evaporation (m2/s2) Hs=Sensible Heat Flux (W/m2)
During the cruise we had no precipitation and therefore Pr was set to zero. Also,
cruise derived water density values were unreliable, so a value of 1025 kg/m3 was
used in the calculations. This was done with the assumption that the salinity error
would be on the order of 0.5% and therefore insignificant in the overall Buoyancy
alculation. Figure [4] is a display of the calculated Buoyancy Flux. c
igure [4]: Buoyancy Flux Time‐series. NOTE: Negative values indicate flux into the ocean.
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F
Several more plots were generated to examine the relationships between the
buoyancy flux values and various other parameters, including ceiling heights. As
expected, buoyancy flux was strongly related to latent heat flux, with a correlation
value of ‐0.952. However, buoyancy flux did not have as strong a correlation to
sensible heat flux, with a correlation value of ‐0.743. While this is a relatively good
correlation, at first this seemed surprisingly weak considering buoyancy flux is also
theoretically dependent on sensible heat flux. The difference is due to the presence
of the surface evaporation term (E), which is a component in the LHF term, and both
buoyancy flux terms. Surface evaporation values had a ‐0.994 correlation with
buoyancy flux.
igure [5]: Normalized Buoyancy Flux vs. Normalized Latent Heat Flux. The expected strong correlation is vident i this time‐series. Fe
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The calculated buoyancy flux values did not have a strong correlation with
ceiling heights. However, when ceiling heights were compared with the heat flux
values, we see stronger correlations. Figure [6] below depicts the strong
relationship between normalized ceiling heights versus the normalized LHF minus
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normalized SHF difference. Normalized values were calculated in the following
manner:
For normalized ceiling height:
Cnorm = <Creg> mean<C> (5)
For normalized heat flux difference:
σC Δ F = (Flhf – Fshf) = <Frl> mean<Flhf> __ <Frs> mean<Fshf> (6) σlhf σshf
σWhere:
lh
x Flhf = Normalized Latent Heat Flux f = LHF Standard Deviation
le Heat Flu hf ation ight viation
Fshf = Normalized Sensib σs = SHF Standard Devi σC = Ceiling Standard De <Frs> = Actual SHF value
Cnorm = Normalized Ceiling He<Frl> = Actual LHF value
<Creg> = Actual Ceiling Height The correlation value for the relationship between ceiling heights and heat flux
differential was calculated at 0.849.
IV. Results:
Eyeball inspection of this plot along with Figure [3] shows that the two
periods of lowest ceiling heights occurred in the early morning hours (local time) of
July 26th and July 27th, and that these low height periods corresponded with a
significant drop in LHF relative to SHF. In taking these two parameters and placing
them into a scatter‐plot, we are able to glean a relationship between the two
parameters. Figure [7] shows the relationship. While the data is certainly
somewhat spread out, a general linear trend can seen between normalized ceiling
heights and normalized heat flux difference (LHF‐SHF). By linear regression
analysis using the ‘polyfit’ function in MATLAB, the following relationship is
expressed:
Hlhfshf = rm) – 0.0013
)
(0.623 • Cno (7)
Where: Hlhfshf = Normalized Flux Difference (Eqn. 6 Cnorm = Normalized Ceiling Height (Eqn. 5)
igure [6]: Time‐series of normalized ceiling heights compared with the difference in normalized flux alues. Fv
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igure[7]: Scatter‐histogram depicting relationship between ceiling height and heat flux difference. he green line represents Eqn. (7) FT
When we view the histograms on the scatter‐plot axis we see that the majority of
data points are located around (0,0). There also tends to be more of a divergence
from the linear relationship at the higher ceiling heights and higher flux difference
(upper right quadrant of data). Further inspection revealed that most of this data
was associated with the first and last 7 hours of our cruise (i.e. during our transit
out and back). If this data is truncated, we can see a slightly different relationship,
shown in Figure [8]. The new linear relationship becomes:
Hlhfshf = (0.512 • Cnorm) – 0.0647 (8)
Figure [8]: Scatter‐histogram depicting truncated ceiling height and flux difference data. The first nd last 400 data points (approximately 7 hrs. encompassing transit into/out of the San Nicholas asin) were removed. aB
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V clusions. Con :
Analysis of flux data strongly suggests a correlation between the relative
difference in latent and sensible heat fluxes, and stratiform ceiling heights. During
the course of our observations strong correlation between latent heat flux and
buoyancy flux was found, but this is not surprising considering that these two
parameters are not independent of each other. On the other hand, little direct
correlation was found between buoyancy flux and cloud ceiling heights. The lack of
a direct relationship between buoyancy flux and ceiling heights is most likely
attributable to the stability of the atmosphere during our cruise. Synoptic‐scale
influences were responsible for the presence of a capping inversion, a strongly
stable atmospheric regime, throughout the operating area around the San Nicholas
Basin. Buoyancy flux is a boundary condition forcing for convective processes.
However, during our cruise, the larger scale stabilizing inversion overwhelmed its
contribution to convective instability. The resulting effect of this scenario is that the
stratiform cloud ceiling parameterization becomes primarily thermodynamic in
nature. In this environment, latent and sensible heat fluxes appear to become
import factors in predicting relative ceiling levels.
V ommendationsI. Rec :
There are several methods by which this study could be extended and
improved upon. All of the results given in this report are based upon the
assumption of no advective effects. This analysis also assumes data was collected at
a single point in space. These assumptions limit analysis to direct one‐to‐one
relationships. Future experiments should incorporate consistent measurements at
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a single point, or at evenly spaced, gridded points in an area of interest. Such an
experimental set‐up would open up the possibility of differential analysis, or at the
very least, a more accurate assessment of how flux differences respond to or force
tratifos rm cloud generation.
This study also did not address the overall state of the atmosphere. Any
further study of stratiform ceiling heights should incorporate an analysis of the
vertical atmospheric structure. Such measurements should take place at the same
times and similar locations to where flux values are being recorded. With these
additions, it may be possible to verify, refute, or refine the linear relationship
observed in this study.
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References
1. udyko, M.I. (1978), The heat balance of the earth, Climatic Change (ed. J. BGribbin), Campbridge Univ. Press, 85‐113.
2. Chu, P.C., & Garwood Jr., R. W. (1990). Thermodynamic Feedback between louds and the Ocean Surface Mixed Layer. Advances in Atmospheric Sciences, CVol. 7 (1), 1‐10.
3. Edwards, Erick, (10 March 2008). The Correlation Between Mixed Depth Layer, Surface Fluxes, and Wind Stress. Retrieved from the OC 3570 Website, http://www.weather.nps.navy.mil/~psguest/OC3570/CDROM/winter2008/Edwards/report.pdf