Contour Plot Flow Direction

How can i plot a quiver plot on top of this to indicate the flow direction. The blue circles are wells and flow is supposed to go downstream.

[darova]

Can you attach something more? The data, code

[Ali Alkoraishi]

clc;clear all;close all
% x and y coordinates of well locations and lake points in cm  (3.4cm/km)
w1=[5.9,5.6];  
w8=[8,7.6];
w17=[11.9,2];
w21=[9.7,5.3];
w27=[4.6,4.6];
w56=[5.9,1.7];
w58=[5.9,1];
w59=[6.7,4.1];
lakepoint1=[4,6.55];
lakepoint2=[5.75,6.9];
lakepoint3=[7.7,7.65];
% Combined coordinates into a single matrix 
wells=[w1;w8;w17;w21;w27;w56;w58;w59;lakepoint1;lakepoint2;lakepoint3];
% Converted well locations to metres
scaledwells=wells*0.441176*1000;
%Groundwater table elevations at each well and at 3 points of the lake. (in metres)
gwtablew1=236.07;
gwtablew8=236.65;
gwtablew17=240.37;
gwtablew21=238.13;
gwtablew27=235.96;
gwtablew56=236.66;
gwtablew58=237.70;
gwtablew59=237.90;;
gwtablelake1=234.19;
gwtablelake2=234.19;
gwtablelake3=234.19;
%Combined into single matrix below
gwtable=[gwtablew1;gwtablew8;gwtablew17;gwtablew21;gwtablew27;gwtablew56;gwtablew58;gwtablew59;gwtablelake1;gwtablelake2;gwtablelake3];
%created scatter plot of x and y coordinates of wells and lake points)
scatter(scaledwells(:,1),scaledwells(:,2))
xlabel('m')
ylabel('m')
grid on
hold on
%Trying to produce contours
scaledwellsx=scaledwells(:,1);
scaledwellsy=scaledwells(:,2);
[X,Y] = meshgrid(sort(scaledwellsx), sort(scaledwellsy));
F = scatteredInterpolant(scaledwellsx,scaledwellsy,gwtable);
Z = F(X,Y);
contour_levels = min(Z,[],'all'):0.2:max(Z,[],'all');
contour(X, Y, Z, contour_levels);

Answer 1

[Adam Danz]

Follow this demo. If you get stuck, show us what you've got and we can help you get un-stuck.

https://www.mathworks.com/help/matlab/creating_plots/display-quiver-plot-over-contour-plot.html

[Ali Alkoraishi]

I tried that with the above link and wasn't sure how to incorporate this part into the above code.

[U,V] = gradient(Z,0.2,0.2);

hold on

quiver(X,Y,U,V)

hold off

[Adam Danz]

You just need to add it after your controur() function. You don't even need to change the variable names.

[Ali Alkoraishi]

This is the output I am getting and its uniform and flowing in the wrong directions, thanks

[Adam Danz]

To create a grid of quiver arrows that flow down hill rather than up hill,

% Grid interp
Xs = linspace(min(scaledwellsx), max(scaledwellsx),20); 
Ys = linspace(min(scaledwellsy), max(scaledwellsy),20); 
[Xq, Yq] = meshgrid(Xs,Ys); 
Vq = F(Xq,Yq);

% Plot quiver grid
% Negate Vq to reverse polarity of vectors
[U,V] = gradient(-Vq); 
hold on
h = quiver(Xq,Yq,U,V,2, 'k') % The 2 is a scaling factor

Notice that gradient(-Vq) reverses the direction of the arrows. You could also try gradient(1./Vq) or use quiverRotate() from the file exchange.