Wikipedia:Reference desk/Archives/Mathematics/2024 May 13

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May 13

Prediction of analogous spatial distributions

Hi guys,

I wish to do a specific GIS/spatial analysis task and I suspect I'm using the wrong search terms in my attempts to figure out existing approaches and tools. Here's what I'm trying to do:

I have a raster data set describing the spatial distribution of a metric in the summer of year X (X1) as well as in the spring (X2). I further have data for the distribution of the same metric in summer only of year Y (Y1). I now want to extrapolate summer raster data of Y1 to Y2. To this end, I want to fit a model to the relationship X1 <-> X2 and then use this model for the prediction Y1 -> Y2. A number of spatial and temporal covariates are available.

I'm guessing that what I'm looking at here would be spatial regression followed by prediction. For the "predict distribution from spatial model" bit, it seems that some flavour of kriging would be suitable, but what I first need is essentially a model describing the transition between two distributions of the same metric (not the spatial relationship of one metric to another in the same space) - seems like a different problem? - To be implemented in QGIS and/or R, if any tool-specific recommendations come to mind.

Cheers! --Elmidae (talk · contribs) 12:08, 13 May 2024 (UTC)

When you make a scatter plot between the X1 and X2 data, do the points seem to lie on a curve with not too much noise? And are the extreme Y1 values not far outside the range of the X1 values? If so, you can simply try curve fitting with a low-degree polynomial and use the curve to read off plausible estimates for the Y2 values. The spatial aspect is then actually irrelevant. It may be relevant for smoothing the observed values before doing anything else. See if this helps with getting a clearer curve. If the metric is necessarily positive, it may further be helpful not to use X1 and X2 directly but to plot instead log(X2) against log(X1). Kriging only plays a role if the summer raster of the years is not the same.  --Lambiam 13:09, 13 May 2024 (UTC)

@Lambiam: sorry for the late response. Thank you, that was helpful! Unfortunately, plotting my data that way showed that the spatial correlation seems to be highly important, as the distribution scatters very widely even with various transformations. Based on what I have read in the meantime, I think a geographically weighted spatial regression is the way to go, if I can get good enough coverage out of my covariates. The prediction bit is going to be interesting since implementations in QGIS seem to be focused on fitting and analysis only, so will have to fully take it to R. --Elmidae (talk · contribs) 11:51, 16 May 2024 (UTC)

Calculus question

Hello there, I'm not sure if this is the right place to ask a calculus question seeming the activity here is quite slim.

A cylindrical tank with a radius of 5 meters is being filled with water at a rate of 3 cubic meters per minute. The tank initially contains 10 cubic meters of water.

1. Write an expression for the volume of water in the tank as a function of time t in minutes.
2. Determine the rate at which the water level is rising in the tank when the depth of the water is 2 meters.
3. At what rate is the water level rising when the tank is half full?

Im lost on the second on here, someone help? GoodHue291 (talk) 22:55, 13 May 2024 (UTC)

Is the the axis of the cylinder horizontal? If so, then more information is needed, such as the length of the tank. catslash (talk) 23:20, 13 May 2024 (UTC)

Yeah, as presented this question is problematic, since for a horizontal axis you need the length, which isn't given, but for a vertical axis the rate, height, pretty much everything is linear. GalacticShoe (talk) 01:28, 14 May 2024 (UTC)

Please do your own homework.

Welcome to Wikipedia. Your question appears to be a homework question. I apologize if this is a misinterpretation, but it is our aim here not to do people's homework for them, but to merely aid them in doing it themselves. Letting someone else do your homework does not help you learn nearly as much as doing it yourself. Please attempt to solve the problem or answer the question yourself first. If you need help with a specific part of your homework, feel free to tell us where you are stuck and ask for help. If you need help grasping the concept of a problem, by all means let us know. - Arjayay (talk) 09:01, 14 May 2024 (UTC)

I put this question here so people can guide me to solving it, they're not going to do it for me. GoodHue291 (talk) 20:32, 14 May 2024 (UTC)

Didn't the reply by 2A01 give you good guidance? What was the expression you found for question 1?  --Lambiam 13:58, 15 May 2024 (UTC)

"The rate at which X is changing" means "the derivative of X with respect to time" where "X" in this case is "the water level". So first you're going to need to find an expression for the water level as a function of time L = f(t) and then work out the derivative of that function to get dL/dt = f'(t). You're also going to need to know the time t at which to evaluate f' which, assuming you know how to convert volume to water level, you can work out using the expression you found in part one. 2A01:E0A:D60:3500:61F0:5F9A:48A:C8D6 (talk) 09:32, 14 May 2024 (UTC)