Step 1: Navigate to your raw/maps/createart/ folder and look for your_mapname_art.gsc. If there is nothing there, then it's in your mod folder.
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Step 2: Open your_mapname_art.gsc and locate the thread fog_settings(). There will be no editing here.

fog_settings()
{
    start_dist = 440;
    halfway_dist = 3200;
    halfway_height = 225;
    base_height = 64;
    red = 0.533;
    green = 0.717;
    blue = 1;
    trans_time = 0;
    if( IsSplitScreen() )
    {
        start_dist = 440;
        halfway_dist = 3200;
        halfway_height = 225;
        cull_dist = 4000;
        maps\_utility::set_splitscreen_fog( start_dist, halfway_dist, halfway_height, base_height, red, green, blue, trans_time, cull_dist );
    }
    else
    {
        SetVolFog( start_dist, halfway_dist, halfway_height, base_height, red, green, blue, trans_time );
    }
}

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Step 3: Copy the code SetVolFog into a separate text editor temporarily and modify it to look like this: start_dist to 440
As you can see, I just copied and replaced the start_dist value with the specific number 440. Do exactly the same for the other values.

SetVolFog( 440, 3200, 225, 64, 0.533, 0.717, 1, 5 ); // Replace trans_time to 5

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Step 4 (Stock): Navigate to your raw/clientscripts/ folder and open your_mapname_fx.csc. If there is nothing there, then it's in your mod folder. Find the threads dog_start_monitor() and dog_stop_monitor(). By default, they should look like this
 
Step 4 (UGX): Navigate to your raw/clientscripts/ folder and open dlc3_code.csc. If there is nothing there, then it's in your mod folder. Find the threads dog_start_monitor() and dog_stop_monitor(). By default, they should look like this

//
// Pulls the fog in
dog_start_monitor()
{
    while( 1 )
    {
        level waittill( "dog_start" );
        //SetVolFog( 75.0, 80.0, 380, -40.0, 0.16, 0.204, 0.274, 7 );
        //SetVolFog( 229.0, 400.0, 115.0, 200.0, 0.16, 0.204, 0.274, 7 );
        SetVolFog( 229.0, 200.0, 380.0, 200.0, 0.16, 0.204, 0.274, 7 );
        //VisionSetNaked(0, "zombie_sumpf_dogs", 7 );
        
    }
}

//
// Pulls the fog in
dog_stop_monitor()
{
    while( 1 )
    {
        level waittill( "dog_stop" );
        SetVolFog( 404.39, 1543.52, 460.33, -244.014, 0.65, 0.84, 0.79, 6 );
        //VisionSetNaked(0, "zombie_sumpf", 4 );
        
    }
}

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Step 5: Inside the dog_stop_monitor() replace the SetVolFog the one you made in other separate text editor. It should be like this

//
// Pulls the fog in
dog_stop_monitor()
{
    while( 1 )
    {
        level waittill( "dog_stop" );
        SetVolFog( 440, 3200, 225, 64, 0.533, 0.717, 1, 5 ); // Replace trans_time to 5
        //VisionSetNaked(0, "zombie_sumpf", 4 );
        
    }
}

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Step 6: If you don't want any dog fog at all, find this and either comment it out or remove it

// level thread dog_start_monitor();
// level thread dog_stop_monitor();