How to prevent decrement (melting) past 0 until growth increases again?

I am creating a snow and ice height time series. Once the snow (hsnow) has completely melted, the energy is used to melt ice (hice). I may be being stupid but I can't seem to find a way to prevent the snow height falling below 0 (as the energy that causes it to decrease past 0 would be used to decrease an ice layer).

Basically once the snow height falls below 0 I want to enforce it at 0 or prevent further decrement past 0, until the snowfall increases again.

hsnow(day+1) = hsnow(day) + snowfall(day) + dh_snow;
h_ice(day+1) = hice(day) + growth(day) + dh_ice;

(dh_snow and dh_ice are the amount of ice and snow melted per day based on the energy available.)

Thanks in advance for any help!

Answer 1

[Image Analyst]

Another way, inside the loop, is to use the max() function:

hsnow(day+1) = max([0, hsnow(day) + snowfall(day) + dh_snow]);
h_ice(day+1) = max([0, hice(day) + growth(day) + dh_ice]);

If either one would be negative, like -5, then it will clip to 0 because the max of -5 and 0 is 0.

[Siân Chilcott]

Ah, thank you amazing! The only issue is when I implement this it throws the error 'Unable to perform assignment because the left and right sides have a different number of elements' - as I calculate temperature by finding the max of the real roots, when I add the max to hsnow it produces no real roots. Although, it's probably hard to diagnose that issue without seeing the code! Thanks for your help!

[Image Analyst]

The only way you could get that error is if dh_snow is a vector, not a single number. Check that. You may need to index it by (day) also.

[Siân Chilcott]

Thanks! I've tried this however, I think the problem is with my temperature calculation. I receive the warning - 0×1 empty double column vector when I use a fourth order polynomial to calculale the temperature, which in turn gives the - 'Unable to perform assignment because the left and right sides have a different number of elements' error, as I have set the temperature to be the max of the real roots. Do you have any ideas on this, as this calculation has run fine until I added in the max line you suggested above?

[Image Analyst]

To help further we'd need your script plus the data.

[Image Analyst]

When I plot some things with the attached script, I get the plots below. Exactly what were you hoping to fit a 4th order polynomial to? And the y on the bottom plot flips slope at one point, going from rising left to right, to falling left to right.

[Siân Chilcott]

So I want to plot hice (Annual Sea Ice Thickness) over a 10 year period. The polynomial uses surface flux data (albedo, otherfluxes and shortwave) to find T_s (temperature) which is then used to find hice.

As ice and snow have different densities I am trying to melt the snow before the ice - this is what the max(0, hsnow) would be used for on line 251. However, when I implement this, the code won't run for more than 2.5 years as the polynomial produces no real roots and I am not sure why that is. I really sorry if my explanation is bad.

I'm not sure what y is as I haven't named any variable as y that I know of - but it looks like its a surface flux.

[Image Analyst]

y is the fourth order polynomial that you'd like to fit. What are you trying to fit a 4th order polynomial to? None of the things I've plotted looks like a 4th order polynomial. Certainly not h_snow or T_b.

[Siân Chilcott]

I want to fit the polynomial to T_s. When I run it for 1 year it looks like the figure below (i've enforced it at 0 for melt reasons). I receive the error I explained earlier when I try and run it for more than one year. I would just like to know why it produces no real roots on day 615.

.

[Image Analyst]

For me it crashes at day 241. Try running the attached script.

Now let's say that I took the values of a, b, c, d, and e when it crashes and extend the days to 500. It would look like the plot in the lower left:

You can see that the 4th order equation has a min of 2.41 which means that it never crosses the x axis and has no real roots. So your code will just have to take that into account.

[Siân Chilcott]

Ah that makes sense - thanks so much for your help!

Answer 2

[Sudheer Bhimireddy]

As soon as you estimated hsnow, force all/any negative values to 0

hsnow(hsnow<0)=0;