Ice cover and severe weather has impeded the gathering of data in the Canadian Archipelago region in the winter months. The density of observations in the WOA and AOA data fields are illustrated in figure 1 of the PHC 2.0 Paper, reproduced here along with a relevant discussion: Paper Figure 1. The lack of winter data available for accurately interpolating onto this region in the WOA and AOA climatologies is evident in this figure.
We used Canadian data from the Bedford Institute to fill this data hole in PHC 2.1. To see the region where we patched this data in, click on the PHC 2.1 image in point #1 of the "Improvements" section, farther down on this page.
PHC 2.0 was created by optimally interpolating the WOA and AOA analyzed fields. Our goal was to retain the WOA field outside of our defined "Arctic Region", while allowing AOA to dominate inside the region. (Page down to see how we defined the Arctic Region in PHC 2.0. Click the PHC 2.0 image to come back.) As a first step in this process, we decimated the WOA field inside the Arctic Region, eliminating all field values where fewer than 2 observations existed. We then interpolated all the remaining WOA field data along with the AOA field data to create PHC 2.0. The schematic below illustrates this procedure.
From these images we see that PHC 2.0 retained WOA's Hudson Bay, which fell outside our Arctic Region. Unfortunately, a lack of data causes the winter WOA in Hudson Bay to be biased towards the more data-rich summer season, i.e. it is too warm (and fresh) in the upper layers in winter. Farther north, we see from the Decimated WOA and AOA input fields that there were no data at all in the Archipelago and Baffin Bay regions. This caused the optimal interpolation routine to revert toward a pre-defined background field. We used a zonally averaged background which worked well around most of the globe, but was too warm for the Archipelago region. In summary, we inherited an overly warm and fresh winter-time Hudson Bay from WOA, as well has introducing some unrealistic values in the Canadian Archipelago by our own methods.
This problem was corrected by incorporating select Canadian data from the Bedford Institute into our optimal interpolation routine. You'll find a summary of how this was accomplished under point #2 of the "Improvements" section, farther down this page.
(Thanks to G. Holloway and N. Steiner)
To create the PHC 2.0 monthly fields, we first had to create AOA monthly fields because they were not available. We then merged these created fields with the WOA monthly fields using the oi routine.
To create the AOA monthly fields, we fit the available seasonal data to a cycloid-sinusoid function. We let the summer values equal August, and the winter values equal April, the extrema of the function. There's a quantitive description of this monthly function in the PHC 2.0 Paper, Creating Monthly AOA Fields.
THE SUBTLE INCONSISTENCY
For the monthly fields to be consistent with the seasonal fields, the average of March, April, and May should be equal to the winter field, and the average of July, August, and September should equal the summer field. In PHC 2.0 this is not the case, because we set April equal to the winter field, and August equal to the summer field. Since April and August are the extrema of the function, the average of the March, April, and May temperature fields, for example, is greater than the winter field. (Since March and May are both greater than April, and April equals winter.) The plots below will make this problem more clear.
The average of Mar, Apr, and May is greater than the winter value. The average of Jul, Aug, and Sep is less than the summer value.
The average of Mar, Apr, and May is less than the winter value. The average of Jul, Aug, and Sep is greater than the summer value.
Our solution to this problem for PHC 2.1 is described under point #3 of the next section. Jump there if you want it now.
Three improvements that make PHC 2.1 better than PHC 2.0
(Reference, if you like, the PHC 2.0 SITE)
For PHC 2.0, the predominate data in the "Arctic Region" was AOA alone. We expanded the "Arctic Region" in PHC 2.1 to include the Canadian Archipelago and surrounding bays, where the Bedford Data was crucial for improving the quality of our winter fields in this region. For an illustration of the specific data coverage contributed from each data source in the Archipelago Region for PHC 2.1, click on the PHC 2.1 image below. Page up to the "PHC 2.0 Winter Temperature" schematic to review the AOA and WOA data coverage for the entire region, or click on the PHC 2.0 image below.
The Arctic RegionThis region represents where PHC differs from the WOA climatology.
Prior to the optimal interpolation, the WOA analyzed fields were decimated inside the Arctic Region where fewer than two observations existed.
For PHC 2.0, we had two main regions to consider when deciding how to assign the optimal interpolation parameters. The PHC paper written for PHC 2.0 describes the primary considerations for determining these parameters. For PHC 2.1, we maintained a similar philosophy in regards to parameters inside and outside the "Arctic Region". Over most of our new PHC 2.1 Arctic Region, we used the same parameters as previously. The table below illustrates these. What changed is how we dealt with the new portion of the Arctic Region in PHC 2.1, the Candian Archipeligo and surrounding bays.
c - correlation length
md - radius of influence
n - number of points used in the calculation
error - Read the caption in figure 3 of the paper for an interpretation of this quantity
|PHC 2.0 Parameters:|
|THE ARCTIC REGION|
c = 500km
|OUTSIDE THE ARCTIC
c = 100km
n = 20
md = 1000km
|THE BOUNDARY REGION
c = 4000km
n = 100
md = 1000km
South of 83.5: error = .0001
South of 83.5: error = .5
The Archipelago region was divided into several subregions, as shown below. It was necessary to subdivide the region to create an accurate background field in all parts of the region. The background field in each region was created from data only in that region. The plot below also illustrates the correlation length scales used in each region, represented by different shades. The table below outlines how relative error values were assigned to each data set in each main region. Low error (say .0001) implies that we trust the data a lot, while high error (say .5) means the opposite. There were not much data available in region 1, even with the addition of the Canadian Data. To compensate for this, we attempted to create high quality background fields in each subregion. At the same time, we stretched the correlation length scale to extend the influence of each data point, while assigning moderate error so that each calculated value would not drift too far from the background field.
The Background Field: Each lettered subregion had a unique background field calculated from values
only in that region. |
Correlation Length Scales (km):
The large length scale in region 1 was necessary to stretch the influence of the sparse data across the region. Some of the subregions have unique characteristics, though, that should not be shared. These subregions were isolated from the others so that they could retain their identity and not influence the rest of the region. This "isolation" was accomplished by increasing the error of all data outside a specific subregion while the oi routine was calculating a value inside the subregion. The data inside the subregion retained all of the relative error values described in the table. When the oi routine moved outside of the isolated subregion, then all of the data inside the subregion was assigned high error, while the data outside returned to the normal error distribution. Read the Optimal Interpolation (OI) Details section of the PHC 2.1 Detailed Report for more information about this.
- The function used to create the AOA monthly fields from the given seasonal fields was modified.
Our goal was to create monthly fields such that the average of March, April and May would equal the winter field, and the average of July, August and September would equal the summer field (read point #3 under the "Motivations" section of this page above). In PHC 2.1, April and August are still the extrema of the cycloid-sinusoid function, but they are no longer forced to equal the winter and summer fields, respectively. Instead, we iterated them until the conditions were both met that the average of March, April, and May was equal to the winter field, and the average of July, August, and September was equal to the summer field. Below are some example plots of how this changed the monthly fields. The dashed line shows the PHC 2.0 monthly series at latitude 89.5, longitude 10.5. The solid line is the PHC 2.1 series at the same location. The averages shown (blue and red dashed line) are the averages of PHC 2.1's March, April, and May, and of July, August, and September. These averages now pass through the winter and summer values, respectively.
Occasionally, below freezing points were introduced into the monthly fields using this technique. This happens because the winter temperature value is already at freezing in many locations. By forcing the average of March, April, and May to equal the winter value, April often had to drop below freezing, as did March, occasionally (as in the left-hand plot below). We corrected this problem by first raising all below-freezing monthly values up to freezing. To ensure that the average of March, April, and May was still equal to the winter value, we then adjusted March and May to compensate for this "warming". First, if March was above freezing (as in situations where only April dropped below freezing after applying our new algorithm - NOT the case in the plot below) , we lowered it to freezing. Then May was lowered until the average of March, April, and May was equal to the winter value. In some instances, this required all three months to be set to freezing. The example in the plots below demonstrates this procedure for the case where both March and April went below freezing when the new algorithm was applied. In this situation, March and April were automatically returned to freezing, and only May had to be adjusted to achieve the winter value average of the three months: freezing.
Another interesting thing to note is that occasionally the winter and summer values are the opposite of what you'd expect them to be. We see this reflected in the above plot on the left, where the salinity minimum is in April, while the maximum is in August. Typically, we'd expect the salinity minimum in August, and the maximum in April. We've looked into this matter, and have concluded that these occasional anomalies (introduced by the AOA fields) may be physically reasonable (or may not). Read more about in the PHC 2.1 Detailed Report: Monthly Fields: Some Additional Details.
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