Project: Due April 30

This project is intended to provide an intriduction to the use of minimization methods in order to produce an analysis of temperature over northern Utah.

The particular case chosen is April 1 1400 UTC (0700 MT), when a strong cold front was approaching the Wasatch. See the following figures for the distribution of observations in the region of interest:

• Intermountain
• Utah
• Wasatch Front
• Salt Lake Valley
• Tooele

The matlab code to start from is available here.

The goal is to produce the best possible analysis of temperature over the entire domain and to assess the sensitivity of the analysis to some of the underlying procedures and assumptions. However, you should use the truncated file for testing and development.

• Example figure (3dvar with decorrelation length scale set to 5km). 5km
• 1. The first part is to incorporate your understanding of Assignment 1 to define some of the parts of the template program that have been left undefined.
  • a. The observation error covariance matrix needs to be defined assuming that the observational errors are not related to one another and the error covariances for each location are the same. In other words, you will have one specified observation error (but allow it, sigo, to be an input variable).
  • b. The background error covariance matrix needs to be defined assuming that the errors decorrelate as a gaussian as before. Use both a parameter for sigb and the decorrelation length scale, rad.
  • Do at least 2 of the following three:
  • c. Initially you can use the definition of the forward transform operator as given in the template code (it simply uses the closest grid point to the observation). However, replace this code eventually with a bilinear interpolation scheme and assess how sensitive the final analysis is to the forward transform operator.
  • d. Modify the code so that the background errors decorrelate with differences in elevation as well as horizontal distance. For example, if the horizontal decorrelation scale is 50 km, use a vertical decorrelation scale of the order of 1km.
  • e. Figure out how to plot the observations on the analysis so that you can see where the observations are adjusting the background.
• 2. Using the updated version of the code used in Assignment 1 (example_3dvar.m), compute a 3DVAR analysis using the conjugate gradient method for the truncated domain. Use a background error decorrelation scale of 50 km and a ratio of the background error variance to the observation error variance equal to 2.
  • a. Where is the background field adjusted the most by the observations?
  • b. Vary the background error decorrelation scale and the background/observation error variance. What are the senstivities to these parameters?
• 3. Generate an analysis for the entire domain (it'll take a bit of computer time). Discuss differences between the background and final analysis as a function of the observations.
• 4. Adapt the existing code to use another type of analysis (OI- it'll take a lot of computer horsepower or Bratseth) or another significantly different linear system solver (quasi-Newton, steepest descent, etc.). Discuss how the solutions differ and differences in the amount of run time required. 5. Read the two papers assigned (MM5 3DVAR and RUC) and discuss briefly in a few paragraphs how the data assimilation is done in each. What are the strengths and weaknesses of the two approaches as described by the authors?
• 6. Email this assignment to me or place your answers, codes, figures, etc. on you personal web page and send me the address. Remember: your code has to run on my workstation!