Differences

This shows you the differences between two versions of the page.

--- kvalobs:kvoss:system:qc2:requirements:nordklim:qc2algorithms [2009-06-25 20:10:08]
paule
+++ kvalobs:kvoss:system:qc2:requirements:nordklim:qc2algorithms [2022-05-31 09:29:32] (current)
@@ Line 1: / Line 1: @@
 ====== Inverse Distance Squared ======
-//... in preparation ...//
+☚ WORKING
+Data from 2007.05.31 to 2007.12.31. For every observed value of 24 hour precipitation at a station a model value is calulated at the same point performing an inverse distance squared weighted interpolation over the nearest neighbours.
+Interpolated_Value = //SUM//[Neighbour_Value/(D*D)] / //SUM//[ 1/(D*D)]
+**D** : The distance between the modeled point and the neighbour station.
+The sum is performed over only the neighbours lieing within 50 km of the model point.
+The graph below depicts the interpolated value at the model point against the actual observed value at that station.
 ^Results  ^
-|{{:kvoss:system:qc2:requirements:nordklim:ids50.jpg|Example results}}|
+|{{kvalobs:kvoss:system:qc2:requirements:nordklim:new_ids50.jpg|Example results}}|
+The same algorithm is applied below but with all neighbours within 100 km distance.
+^Results  ^
+|{{kvalobs:kvoss:system:qc2:requirements:nordklim:new_ids100.jpg|}}|
+... and if no range limit is applied (i.e. interpolate over all possible neighbours).
+^Results  ^
+|{{kvalobs:kvoss:system:qc2:requirements:nordklim:new_idsall.jpg|}}|
+====== Inverse Distance Squared (with Height Correction) ======
+The same algorithm is applied as for normal inverse distance square weighting except that all observations are reduced to a modelled value at sea-level, the interpolation is performed, and the result is scaled back to the interpolated point real altitude.
+For all altitudes below 1000 m the precipitation value decreases by 10% per 100m altitude, above 1000m the change is 5% per 100m.
+^Results  ^
+|{{kvalobs:kvoss:system:qc2:requirements:nordklim:ids50ht_v828.jpg|}}|
+====== Linear Interpolation over neighbours selected by Delaunay Interpolation ======
+For a given point all neighbours with valid measurements (i.e. no missing values) are analyzed. A Delaunay Triangulation is applied to find the best three neighbours corresponding to the point of interest (e.g. [[.qc2algorithms:delaunay| Delaunay Example]]) and the constraint of fitting triangles to all the stations in the neighbourhood. The neighbourhood is constrained to be a limited number of stations that lie within a fixed distance of point of interest (e.g. 50 km in the example below).
+Linear interpolation is then performed as follows (details courtesy of MM).
+<code>
+  Denom=(x3-x1)*(y2-y1)-(x2-x1)*(y3-y1)
+  d_rr_over_d_x=((y2-y1)*(rr3-rr1)-(y3-y1)*(rr2-rr1))/Denom
+  d_rr_over_d_y=((x3-x1)*(rr2-rr1)-(x2-x1)*(rr3-rr1))/Denom
+  rr=rr1+(x-x1)*d_rr_over_d_x+(y-y1)*d_rr_over_d_y
+</code>
+where x1, x2, x3 and y1, y2, y3 are the x and y coordinates of the three
+points of the triangle of interest. x and y are the coordinates of the point
+where RR is to be calculated. rr is the calculated precipitation.
+^Results  ^
+|{{kvalobs:kvoss:system:qc2:requirements:nordklim:new_tri50.jpg|}}|
+====== Wet or Dry Separation ======
+FIXME
+^Results  ^
+|{{kvalobs:kvoss:system:qc2:requirements:nordklim:wetdry.jpg|}}|
+====== Sanity Check ======
+The following graphs includes simulated data to check the validity of the statistical values encoded.
+{{kvalobs:kvoss:system:qc2:requirements:nordklim:new_noisyfit.jpg|}}
+{{kvalobs:kvoss:system:qc2:requirements:nordklim:new_superfit.jpg|}}
+====== Binned Averages and Standard Deviation Bars ======
+{{kvalobs:kvoss:system:qc2:requirements:nordklim:bin_ids100.jpg|}}
+{{kvalobs:kvoss:system:qc2:requirements:nordklim:bin_ids50.jpg|}}
+{{kvalobs:kvoss:system:qc2:requirements:nordklim:l50h-ids-scatter.jpg|}}
+{{kvalobs:kvoss:system:qc2:requirements:nordklim:bin_idsall.jpg|}}
+{{kvalobs:kvoss:system:qc2:requirements:nordklim:bin_tri50.jpg|}}
+{{kvalobs:kvoss:system:qc2:requirements:nordklim:q-wd50.jpg|}}
+ --- // 2009/11/01 01:09 //
+{{kvalobs:kvoss:system:qc2:requirements:nordklim:all-ids.nc.jpg|}}
+{{kvalobs:kvoss:system:qc2:requirements:nordklim:delaunay-linear.nc.jpg|}}
+{{kvalobs:kvoss:system:qc2:requirements:nordklim:l50-ids.nc.jpg|}}
+{{kvalobs:kvoss:system:qc2:requirements:nordklim:l50h-ids.nc.jpg|}}
+{{kvalobs:kvoss:system:qc2:requirements:nordklim:wetdry50-ids.nc.jpg|}}