I have the same problem with Barnes surface, but I was successful with
Heatmap. So you can try Heatmap instead of Barnes surface. The function may
work different than interpolation, but may be useful for you purposes (I do
not know them). 

<StyledLayerDescriptor version="1.0.0"
       xsi:schemaLocation="http://www.opengis.net/sld
StyledLayerDescriptor.xsd"
       xmlns="http://www.opengis.net/sld";
       xmlns:ogc="http://www.opengis.net/ogc";
       xmlns:xlink="http://www.w3.org/1999/xlink";
       xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance";>
     <NamedLayer>
       <Name>Heatmap</Name>
       <UserStyle>
         <Title>Heatmap</Title>
         <Abstract>A heatmap surface showing population density</Abstract>
         <FeatureTypeStyle>
           <Transformation>
             <ogc:Function name="gs:Heatmap">
               <ogc:Function name="parameter">
                 <ogc:Literal>data</ogc:Literal>
               </ogc:Function>
               <ogc:Function name="parameter">
                 <ogc:Literal>weightAttr</ogc:Literal>
                 <ogc:Literal>cat</ogc:Literal>
               </ogc:Function>
               <ogc:Function name="parameter">
                 <ogc:Literal>radiusPixels</ogc:Literal>
                 <ogc:Function name="env">
                   <ogc:Literal>radius</ogc:Literal>
                   <ogc:Literal>100</ogc:Literal>
                 </ogc:Function>
               </ogc:Function>
               <ogc:Function name="parameter">
                 <ogc:Literal>pixelsPerCell</ogc:Literal>
                 <ogc:Literal>10</ogc:Literal>
               </ogc:Function>
               <ogc:Function name="parameter">
                 <ogc:Literal>outputBBOX</ogc:Literal>
                 <ogc:Function name="env">
                   <ogc:Literal>wms_bbox</ogc:Literal>
                 </ogc:Function>
               </ogc:Function>
               <ogc:Function name="parameter">
                 <ogc:Literal>outputWidth</ogc:Literal>
                 <ogc:Function name="env">
                   <ogc:Literal>wms_width</ogc:Literal>
                 </ogc:Function>
               </ogc:Function>
               <ogc:Function name="parameter">
                 <ogc:Literal>outputHeight</ogc:Literal>
                 <ogc:Function name="env">
                   <ogc:Literal>wms_height</ogc:Literal>
                 </ogc:Function>
               </ogc:Function>
             </ogc:Function>
           </Transformation>
          <Rule>
            <RasterSymbolizer>
            
              <Geometry>
                <ogc:PropertyName>the_geom</ogc:PropertyName></Geometry>
              <Opacity>0.6</Opacity>
              <ColorMap type="ramp" >
                <ColorMapEntry color="#FFFFFF" quantity="0" label="nodata"
                  opacity="0"/>
                <ColorMapEntry color="#FFFFFF" quantity="0.02"
label="nodata"
                  opacity="0"/>
                <ColorMapEntry color="#4444FF" quantity=".1"
label="nodata"/>
                <ColorMapEntry color="#FF0000" quantity=".5" label="values"
/>
                <ColorMapEntry color="#FFFF00" quantity="1.0" label="values"
/>
              </ColorMap>
            </RasterSymbolizer>
           </Rule>
         </FeatureTypeStyle>
       </UserStyle>
     </NamedLayer>
    </StyledLayerDescriptor>

<http://osgeo-org.1560.x6.nabble.com/file/n5272624/heatmap.png> 



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