Differentiation question - How to find out H vs. dH/dt from a list of height and datetime series?

Hi!

I have a fundamental differentiation problem. I need to find out the derivative of the tide height (H) with repsect to time (t). The heights are in meter and the times are in datetime format.

H = [1.164;0.819;0.389;0.023;-0.123;-0.081;-0.039;...
    0.118;0.272;0.515;0.892;1.301;1.572;1.573;1.576];

and the time series, T is -

'01-Jan-2003'
'17-Jan-2003'
'03-Feb-2003'
'20-Feb-2003'
'01-Mar-2003'
'15-Mar-2003'
'04-Apr-2003'
'16-Apr-2003'
'30-Apr-2003'
'15-May-2003'
'01-Jun-2003'
'16-Jun-2003'
'03-Jul-2003'
'18-Jul-2003'
'05-Aug-2003'

Can anyone please give me an idea on how can I plot the H vs. dH/dt? Any feedback will be greatly appreciated!

Answer 1

[Star Strider]

One approach —

T = ['01-Jan-2003'
'17-Jan-2003'
'03-Feb-2003'
'20-Feb-2003'
'01-Mar-2003'
'15-Mar-2003'
'04-Apr-2003'
'16-Apr-2003'
'30-Apr-2003'
'15-May-2003'
'01-Jun-2003'
'16-Jun-2003'
'03-Jul-2003'
'18-Jul-2003'
'05-Aug-2003'];

H = [1.164;0.819;0.389;0.023;-0.123;-0.081;-0.039; 0.118;0.272;0.515;0.892;1.301;1.572;1.573;1.576];

DT = datetime(T)

DT = 15×1 datetime array
   01-Jan-2003
   17-Jan-2003
   03-Feb-2003
   20-Feb-2003
   01-Mar-2003
   15-Mar-2003
   04-Apr-2003
   16-Apr-2003
   30-Apr-2003
   15-May-2003
   01-Jun-2003
   16-Jun-2003
   03-Jul-2003
   18-Jul-2003
   05-Aug-2003

DOY = day(DT,'dayofyear')

DOY = 15×1

1 17 34 51 60 74 94 106 120 135

dHdT = gradient(H) ./ gradient(DOY);

figure
yyaxis left
plot(DT, H)
ylabel('Height', 'Interpreter','latex')
yyaxis right
plot(DT, dHdT)
ylabel('$\frac{dH(T)}{dT}$', 'Interpreter','latex')
grid

.

[Ashfaq Ahmed]

This is a brilliant approach! Thank you so much for the code! But can you please tell me what happens when I work with multiple year's data? I think the only limitation of this code can be the conversion to the "date of the year" array. How can I proceed with when I have many year's of data?

[Star Strider]

As always, my pleasure!

One option is to use datenum, however as much as I would like it to be possible to do this with a duration array, that does not appear to be an option, although it should be possible.

One way to hack it —

T = ['01-Jan-2003'
'17-Jan-2003'
'03-Feb-2003'
'20-Feb-2003'
'01-Mar-2003'
'15-Mar-2003'
'04-Apr-2003'
'16-Apr-2003'
'30-Apr-2003'
'15-May-2003'
'01-Jun-2003'
'16-Jun-2003'
'03-Jul-2003'
'18-Jul-2003'
'05-Aug-2003'];

DT = reshape(datetime(T) + calyears(0:2), [],1)     % Create Date Data For Multiple Years

DT = 45×1 datetime array
   01-Jan-2003
   17-Jan-2003
   03-Feb-2003
   20-Feb-2003
   01-Mar-2003
   15-Mar-2003
   04-Apr-2003
   16-Apr-2003
   30-Apr-2003
   15-May-2003
   01-Jun-2003
   16-Jun-2003
   03-Jul-2003
   18-Jul-2003
   05-Aug-2003
   01-Jan-2004
   17-Jan-2004
   03-Feb-2004
   20-Feb-2004
   01-Mar-2004
   15-Mar-2004
   04-Apr-2004
   16-Apr-2004
   30-Apr-2004
   15-May-2004
   01-Jun-2004
   16-Jun-2004
   03-Jul-2004
   18-Jul-2004
   05-Aug-2004

csDOY = cumsum(day(DT,'dayofyear'))                 % Cumulatively Sum 'dayofyear'

csDOY = 45×1

1 18 52 103 163 237 331 437 557 692

dT = gradient(csDOY,1)                              % Then, Calculate 'gradient'

dT = 45×1

17.0000 25.5000 42.5000 55.5000 67.0000 84.0000 100.0000 113.0000 127.5000 143.5000

H = sin(2*pi*csDOY*(0.25/365))*1.5;                 % Simulate Tide Height
dH = gradient(H,(1/365));                           % Then, Calculate 'gradient'

figure
yyaxis left
plot(DT, H)
ylabel('Height', 'Interpreter','latex')
yyaxis right
plot(DT, dH./dT)
ylabel('$\frac{dH(T)}{dT}$', 'Interpreter','latex')
grid

There should be a more straightforward way to calculate cumulative days across multiple years using datetime or duration arrays. If there is, it’s quite well hidden in the documentation, at least from me.

In this instance, it might still be easier to convert the datetime array to a datenum array before calculating the gradient. That would be worth considering.

My apologies for the delay, however it took a while to come up with this approach.

.