Tuesday, April 14, 2009

Advanced Hydrology Term Project

For Advanced Hydrology we were given a semester project to work on. A big, long one that will require a lot of our time to do. In addition to the project, we have to create a presentation and write a fancy report. As a term project, you would expect us to have the entire term to be working on it, but, unfortunately that is not the case for Advanced Hydrology. We got the project on Monday. That's seven-days-until-the-end-of-the-semester Monday. Allow me to explain through question 1.


Note: The first order Markov Model (order p=1) for Normally distributed flows can be expressed as: Xi,j+1=ux,j+1+px,j(1)*(sx,j+1/sx,j)*(Xi,j-ux,j)+tx,j+1*sx,j+1*sqrt(1-(px,j(1)^2)

Using both monthly flows Xi,j and Zi,j series at the streamflow gauging site:

i. Plot the time series

ii. Compute basic statistics like the mean, standard deviation, coefficient of skew and correlation coefficients between monthly flows. Note: This step will require the use monthly flows grouped by month like January together etc for series.

iii. Compute the auto-correlogram of the Zi,j series for a maximum of 12 lags of the time series treating it as a stationary series with no periodicity. Note: This step will treat the monthly flows as one combined time series. Hence the lags are accomplished by simply lagging the series by 1,2,3...12 times. Compare and comment on the differences between the auto-correlation for different lags from 1,2...12 with thos obtained for each month in Step (ii) above.

iv. Use the monthly correlation coefficient matrix from Step (i) to identify the order p for the Auto Regressive (AR) model both series.

v. Write out the complete format for the Autoregressive model to give Xi,j and Zi,j as a function of previous values of {Xi,j-1,Xi,j-2,...} or {Zi,j-1,Zi,j-2....} and other required components. This will look like the Markov Model (Eq. 15.17 which is for order 1, page 378 with additional lags if needed (see secion on Higher order Autoregressive models on page 379-380 equation 15.20 and 15.21, text). Note: If you have more than one order 1-R^2 term in Eq. 15.21 will be (1-p(1)^2-p(2)^2...)


Everything above is typed as it appears on my sheet. The boldface is boldfaced. The typos are typo-d. Is it just me, or does reading through that stuff make your head hurt? I'm in a hydrology class, not an advanced statistics class. This entire semester has been statistics, statistics, probability, and more statistics. The only thing that makes it hydrologically related is the fact that we use streamflow data for our data to run statistical models on.

The ironic thing is I kind of enjoyed some of the statistical methods back at the beginning of the class. When we were running simple regression and analysis. Generating hypothesis tests. And then we got in to this weird, higher order stuff, and the entire class lost it.

Ah, well. I guess I'm supposed to complain. All students do, right? I've made it this long, with just o'er a week to go until school is done, so I can handle it. Once I get through question 1, I'll have question 2 to worry about.

Until then, I'll just keep on a chooglin.

No comments: