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You can loop over every vertex after initializing different arrays for each of your vertex color layers. You can parse the init data from a file (eg .csv) with python but this is not covered in this answer.

import bpy
import bmesh

obj = bpy.context.selected_objects[0]  # Get the currently selected object

vertex_colors = obj.data.vertex_colors
while vertex_colors:
    vertex_colors.remove(vertex_colors[0])  # Remove all vertex color layers form the mesh data

bm = bmesh.new()  # Create new bmesh object
bm.from_mesh(obj.data)  # Init the bmesh with the current mesh

verts_count = len(bm.verts)  # Get the number of vertices in the mesh 
# Not obligatory, I just use this to populate the vertex color layers)

# This dictionary will map each vertex color layer name to the data for each vertex
data_layers = {
    'Temperature':  # vertex color layer name 1
        [
        (1, 0, 0, 1),  # Color of vertex index 1
        (0, 1, 0, 1),  # Color of vertex index 2
        (0, 0, 1, 1),  # Color of vertex index 3
        (1, 1, 1, 1),  # Color of vertex index 4...
        ],    
    'Velocity':  # vertex color layer name 2
        [(i / verts_count, i / verts_count, i / verts_count, 1) for i in range(verts_count)],
    'Salinity':  # vertex color layer name 3
        [(i / verts_count, 1 - (i / verts_count), 0.5, 1) for i in range(verts_count)],        
    }

color_layers = {}
for layer_name in data_layers:
    # Create the vertex color layers and store them in a dictionary for easy access by name
    color_layers[layer_name] = bm.loops.layers.color.new(layer_name)

for layer_name, layer in color_layers.items():
    # Loop over each vertex color layer
    for v in bm.verts:
        # Loop over every vertex
        for loop in v.link_loops:
            # Loop over every loop of this vertex (the corners of the faces in which this vertex exists)  
            try:
                loop[layer] = data_layers[layer_name][v.index]
                # Get the value from the init dictionary
            except IndexError:
                loop[layer] = (1, 0, 1, 1)
                # Set a placeholder (magenta) value if the mapping array is not long enough

bm.to_mesh(obj.data)  # Give the data back to the actual mesh

Then to acces the vertex colors in your material, use the vertex color node :

Note that the "Temperature" layer was initialized with only 4 values, so only a few vertices in the right eye got colored and the rest of the vertices got mapped to a magenta color.