July 20, 2007
ΔP vs. ΔZ Reanalysis and Analysis charts contained in 072007_delpvgeostrophic_v2.xls.
Analysis vs. Reanalysis
Pressure Difference: In both the analysis and reanalysis I used the observed pressure difference from Tatoosh
Island on the west end of the Strait and Whidbey Island near the east end of the Strait. I used the time of maximum
pressure difference made sure that it was close to the time of maximum wind speed. In most cases these lined up but
in a few cases I used my best judgment on which time to use. The only problem this presented was if the time fell in
between 6 hourly reanalysis grids but the high wind observation did not.
Reanalysis: Initially, I calculated the height difference across the middle of the Strait (shore to shore and
perpendicular to the axis of the Strait) using the NCEP 850mb reanalysis grids which are available every 6 hours
(00, 06, 12, and 18Z). I chose which chart to use based on the time which was closest to the highest recorded wind
at any one of our stations. If that wind observation fell halfway in between (i.e. 15Z) then I calculated the height
difference across the Strait for the 2 nearest times (i.e. 12Z and 18Z) and averaged the results.
http://www.cdc.noaa.gov/Composites/Hour
Analysis: To double check the accuracy of the reanalysis grids, I calculated the height difference across the Strait
using the NOAA 850mb analysis charts which are available every 12 hours. I chose the chart based on the time
nearest to the maximum pressure difference or highest observed wind speed at any of our stations. Again, if that
time fell halfway between the two available chart times I used both charts to calculate a height difference and
averaged the results. Due to the resolution of these particular charts around the Strait, I calculated the height
gradient over a larger distance, not just from shore to shore. I calculated this distance from 46N, 124W to 51N,
122.5W. This distance is roughly 566 km and the linear path between these two points is roughly perpendicular to
the axis of the Strait of Juan de Fuca. In some cases the gradient over this distance was not uniform. I have not
decided what to do about this yet.
http://nomads.ncdc.noaa.gov:9091/ncep/NCEP
Plot Descriptions
ΔP vs. ΔZ @ 850mb – Reanalysis: In each of these 3 plots I plotted all of the data together, both winter and
summer storms. Due to this fact, I needed to differentiate between winter and summer storms. I did this with the
shape of the point. Summer storms are indicated with a CIRCLE and winter storms are indicated with a
DIAMOND. Since this is a pressure gradient plotted against a height gradient, there is no indication of wind speed
in this plot. If the wind speed for that storm was 40 kts to 49 kts the color of the point was changed to RED. Below
40 kts the color of the point is BLUE. For 50 kts and above the point is GREEN.
Plot 1 – Labels are <storm date, wind speed (kts)>.
Plot 2 – Labels are <wind speed (kts)>. This is mostly just for plot cleanliness.
Plot 3 – No labels. Trend line included and points with no ΔP are omitted.
ΔP vs. Wind Speed – Reanalysis: In this plot the winter and summer dates are plotted separately so that trend lines
could be used on each group. The winter storms are all plotted with BLUE DIAMONDS and the summer storms are
plotted in RED CIRCLES. The trend line in this particular plot is only for the winter storms. However, the summer
trend line lies directly on top of the winter one, so I removed it for cleanliness. There are no labels associated with
each point due to the density of the points. Points without complete ΔP observations are omitted for the purposes of
establishing a more accurate trend line.
ΔZ vs. Wind Speed – Reanalysis: Again, in this plot both winter and summer dates are separated so trends can be
established for each set of storms. Winter dates are indicated with BLUE DIAMONDS and summer dates are
indicated with RED CIRCLES. There are no labels associated with each point due to the density of the points. The
ORANGE trend line is indicating the winter storm trend. The Red trend line is indicating the summer storm trend.
No data is omitted as reanalysis charts were available for each of our selected storms.
ΔP vs. ΔZ @ 850mb – Analysis: Unlike the reanalysis plots, there is just one plot here which includes labels with
dates and wind speeds. The data set plotted includes both summer and winter points together so the ORANGE trend
line is indicative of the entire set of points. Summer storms are indicated with a CIRCLE and winter storms are
indicated with a DIAMOND. Since this is a pressure gradient plotted against a height gradient, there is no
indication of wind speed in this plot the wind speed for that storm was 40 kts to 49 kts the color of the point was
changed to RED. Below 40 kts the color of the point is BLUE. For 50 kts and above the point is GREEN. Points
without complete pressure gradient data are not included in this plot.
ΔP vs. Wind Speed – Analysis: In this plot the winter and summer dates are plotted separately so that trend lines
could be used on each group. The winter storms are all plotted with BLUE DIAMONDS and the summer storms are
plotted in RED CIRCLES. The ORANGE trend line is indicating the winter storm trend. The Red trend line is
indicating the summer storm trend. There are no labels associated with each point due to the density of the points.
Points without complete ΔP observations are omitted for the purposes of establishing a more accurate trend line.
ΔZ vs. Wind Speed – Analysis: Again, in this plot both winter and summer dates are separated so trends can be
established for each set of storms. Winter dates are indicated with BLUE DIAMONDS and summer dates are
indicated with RED CIRCLES. There are no labels associated with each point due to the density of the points. The
ORANGE trend line is indicating the winter storm trend. The Red trend line is indicating the summer storm trend.
The data set is not quite complete because only storms with analysis charts available on the internet were used. This
excludes any storms that were prior to 1998. I am currently working on getting charts for the other storms and will
update this plot when the data is available.
Analysis vs. Reanalysis: This plot is simply to demonstrate how accurately the two methods for calculating the
geostrophic wind line up. On average, the reanalysis method tends to predict slightly higher geostrophic winds. The
GREEN line indicates 1:1 or y = x. The ORANGE line is the linear regression (or trend line) of the data.
Data
Reanalysis: The ΔZ in this data set was measured from shore to shore across the middle of the Strait and
perpendicular to the axis of the Strait using the NCEP reanalysis grids available every six hours. The geostrophic
wind is then calculated in m/s using the formula below:
𝑣g =
𝑔0 𝜕𝑧
𝑓 𝜕𝑛
Where, g0 = -9.81 m/s2, f = 2Ωsinφ = 0.00010889, ∂n = 22,500 m. φ is the latitude north in the middle of the Strait
(~48.3°N). The resulting geostrophic wind speed is then converted to kts. The ΔP is taken from another spread
sheet where it was calculated as the difference between the observed pressure at Tatoosh Island and Whidbey Island.
Analysis: The ΔZ in this case was calculated using the national weather service 850mb analysis charts taken every
12 hours, from 46N, 124W to 51N, 122.5W, a 566 km distance. This straight line distance is roughly perpendicular
to the W-E axis of the Strait. The geostrophic wind is then calculated using the equation above. In this case,
however, ∂n = 566,000 m. The resulting geostrophic wind speed is then converted to kts. The ΔP is taken from
another spread sheet (the same as above) where it was calculated as the difference between the observed pressure at
Tatoosh Island and Whidbey Island. In the ∂z column, there are some highlighted cells. If the cell is highlighted
YELLOW, the distance is averaged over two charts. If the cell is highlighted RED, it was noticed that the height
gradient over the measured distance was not uniform. If the cell is highlighted ORANGE, there is a combination of
the above two issues, the gradient is not uniform on one or more of two charts which are averaged together.