253 lines
13 KiB
HTML
253 lines
13 KiB
HTML
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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<html>
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<head>
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<meta http-equiv="CONTENT-TYPE" content="text/html; charset=utf-8">
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<title>ModelBlend</title>
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<meta name="GENERATOR" content="OpenOffice.org 1.1.3 (Linux)">
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<meta name="CREATED" content="19951121;16410000">
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<meta name="CHANGED" content="20050706;13040400">
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</head>
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<body dir="ltr" lang="de-DE" text="#000000">
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<font face="New Century Schoolbook, Times New Roman, serif"><font
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size="5"><b>ModelBlend</b></font></font>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif"><font
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size="3"><b>Introduction</b></font></font>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">Sometimes it is desirable
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to average grids from different models, different runs, etc. This tool allows you to
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make a weighted average of many grids, including the forecast, official, and model
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grids. Complex weighted averages can be constructed in a single step, and model
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extrapolations can also be constructed. The tool has the ability to blend
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inside an edit area rather than over the entire grid, and to apply ‘edge effects’ to
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the blending in those areas – so that they blend in smoothly with unmodified points
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outside the edit area. The tool can be used on any scalar or vector grid.
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When used on a vector grid, the vector is changed into components before performing
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the weighted average, then transformed back to the normal vector grid.</font>
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<br>
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<br>
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<br>
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<big><big><font style="font-weight: bold;"
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face="New Century Schoolbook, Times New Roman, serif">How
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the Procedure Works</font><span style="font-weight: bold;">
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</span></big></big><br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">Lets say we start with a
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Fcst minimum temperature forecast grid that looks like this:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend1.jpg"></font>
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<br>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">Now suppose that the latest
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ADJMEX model forecast grid for the same period (a 6-day forecast) looks like this:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend2.jpg"></font>
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<br>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">The difference between
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these two grids is very complex:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend3.jpg"></font>
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<br>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">Now, suppose we somewhat
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believe this ADJMEX model forecast. However, since it is a day-6 forecast, we want
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to slowly nudge our forecast grid toward the ADJMEX solution, rather than adopt
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the ADJMEX grid completely. The Model_Blend tool allows us to make a weighted
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average of our current Forecast Grid and this ADJMEX forecast grid.</font>
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<br>
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<br>
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<br>
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<big><big><font face="New Century Schoolbook, Times New Roman, serif"><b>Running
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the Procedure</b></font>
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</big></big><br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">When the Model_ Blend tool
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is started, a dialog appears where you can specify weights for various forecast,
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official and model grids:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend4.jpg"></font>
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<br>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">Note that the default it to
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weight the forecast grid with a value of one, and all other grids with a value of zero.
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Thus, if nothing on this dialog were changed, and the tool run (by clicking on the Run
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or Run/Dismiss buttons), then the forecast grid would be returned unchanged.<br><br>
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In this case, suppose we want to evenly weight the current forecast grid and the latest
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ADJMEX forecast grids that were shown above. We could change the slider weights to
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indicate this:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend5.jpg"></font>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">Weighting the grids evenly
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means that a simple average is being performed. The average grid comes out:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend6.jpg"></font>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">If you carefully look at the
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sample points, you will see that the grid is an average of the Forecast and ADJMEX grid.
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<br><br>
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Note that in this case we set the weights to one for both the Forecast and the ADJMEX
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grid. We could have easily weighted them both ten, and the result would be the same.
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The magnitude of the weights is irrelevant in this case, the fact that the weights are
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equal means that a simple average is performed.
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<br><br>
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Suppose, instead, that we wanted to weight our average more strongly toward the new
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model solution. We could set the weights such that the ADJMEX model is weighted with
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a value of three, and the current forecast with a value of one.<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend7.jpg"></font>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">Since there are four total
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units, and the ADJMEX receives three and the current forecast one, the ADJMEX will make
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up 75% of the new grid (3/4) and the current forecast will make up 25% (1/4) of the new
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grid. The new weighted average looks like:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend8.jpg"></font>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">Suppose, instead, that we
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want to evenly weight the current ADJMEX 6-day forecast, with the 7-day forecast from
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the previous ADJMEX run. This evenly accomplished by setting the weights equally in
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the Model_Blend dialog:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend9.jpg"></font>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">Note that we set the weight
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for the current forecast to zero - indicating that we want only the average of the two
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ADJMEX runs. The two ADJMEX forecast grids look like this:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend10.jpg"></font>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">The resulting simple average
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of these two grids becomes:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend11.jpg"></font>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">The weight sliders can be
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configured to allow negative values. Negative weights allow you to perform model
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extrapolations. Consider, for example, only the sample value at Burns, Oregon
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(the westernmost sample point on the images). The current ADJMEX run forecasts
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44 degrees for this point, while the previous run forecast 41 for this point.
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The ADJMEX forecasts are getting warmer. One could argue that the best forecast
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might be even warmer than the 44 degrees forecast by the latest ADJMEX run.
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A simple extrapolation can be performed by making the weight for the earlier run
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negative, and half as large as the current run. For example, we can set the weight
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for the latest run to two, and the weight for the earlier run to negative one:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend12.jpg"></font>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">Consider, again, only
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the point for Burns, Oregon. The new value will be (2*44) + (-1*41) = 47.
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The trend of warming 3 degrees is continued for 3 more degrees of warming.
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This is performed individually at every gridpoint. Some gridpoints cooled between
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the first run and the second run, and likewise at those locations, the cooling is
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extrapolated to the final grid. The resulting grid looks like this:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend13.jpg"></font>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">Note that the sample value
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at Burns, Oregon turned out to be 47, just as we calculated above.
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<br><br>
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A simple extrapolation, as described above may be too extreme. Again, considering
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only the forecast for Burns: the 7-day forecast was 41 and the 6-day forecast was 44.
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If you believe that such a trend will continue, then the 5-day forecast will be 47,
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the 4-day forecast will be 50, the 3-day forecast will be 53, the 2-day forecast
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will be 56, the 1-day forecast will be 59, and the final temperature will be 72.
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Such a procedure is clearly nonsense. The 6-day forecast of 44 is warmer than the
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earlier run, but it is the best forecast that the model can provide at that time.
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While extrapolating the trend somewhat might be reasonable, extending it indefinitely
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is foolish.
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<br><br>
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Suppose that we want to use some of the trend, but weight the combination strongly
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toward the value in the latest forecast. Again, you can use negative weights on an
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earlier forecast, but much larger positive weights on the latest forecast.
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For example, if we weight the new forecast with a value of eight, and the old
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forecast with a value of negative one:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend14.jpg"></font>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">The resulting grid looks like:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend15.jpg"></font>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">Note that the extrapolation
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makes a forecast of 44 at Burns. The continuation of the trend is so small that it
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is indistinguishable from the latest ADJMEX forecast.
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<br><br>
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More than two grids can be combined using the Model_Blend tool. You can set equal
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weights for all grids, and get a simple average of all model forecasts. Very complex
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weighting schemes that weight one model more heavily than others can also be
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accomplished.
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<br><br>
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New in version 2.0 of the tool, is the ability to apply the blend over the current
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edit area, rather than the entire grid. For example, here we display an edit area
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over both the current Fcst grid and the ADJMEX grid.<br><br>
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Current Fcst Grid:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend16.jpg"><br><br>
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ADJMEX Grid:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend17.jpg"></font>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">If we specify the
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weights in Model_Blend dialog to be zero for the Fcst grid and one for the ADJMEX
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grid (essentially copying the ADJMEX grid into the Fcst grid – but only inside the
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edit area):<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend18.jpg"></font>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">Then the resulting grid becomes:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend19.jpg"></font>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">Note that because we
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specified “Flat” (the default) that some intense temperature “gradients” were
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introduced. This is because the model data copied inside the edit area does not
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match with the original Fcst grid outside the edit area. There are two ways to
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mitigate this problem.
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<br><br>
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First, you can specify an “edge” behavior inside the edit area where “blending” will
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taper back to zero, (and you can specify the edge width – in pixels) such as:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend20.jpg"></font>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">Where the default edge
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width of 5 pixels is chosen. The resulting grid comes out:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend21.jpg"></font>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">Note that there are no
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extreme “gradients” and that within 5 pixels of the edge of the edit area, the r
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esulting grid is a blend of the ADJMEX grid and the Fcst grid.
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<br><br>
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If, instead, you would like only the center of the edit area to get the full Model
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Blend that you specify – and taper back smoothly to the original grid at the outer
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edge of the edit area, then you could specify “Taper” in the dialog:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend22.jpg"></font>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">Here the resulting grid comes out:<br>
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<img alt="ModelBlend User Interface" src="images/ModelBlend23.jpg"></font>
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<br>
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<br>
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<font face="New Century Schoolbook, Times New Roman, serif">One important restriction on
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your weights is enforced: the weights cannot add up to zero. You cannot weight one
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model with positive one and another with negative one, because the total weight would
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be zero. This can also occur if model data cannot be read from the database - in
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which case the weight for that model run is removed from the overall weights.
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Care should be take to use the tool with model grids that exist - and with
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combinations of weights that do not add to zero.
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<br><br>
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</font>
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</body>
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</html>
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