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MULTIFRACTALS AND PHYSICALLY BASED ESTIMATES OF EXTREME FLOODS Phase 4A. Prepared by Physics Department, McGill University Montreal, Quebec Principal Investigator Shaun Lovejoy. Goal of the project. Overall goal of the project:
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Physics Department, McGill University
Overall goal of the project:
Phases 1A, 1B, 1C have focused on developing this theory for river series with weak annual cycles and demonstrating it on data series.
Extremes (red), from power law tail
A plot of the streamflow series vs. time for Uchee Creek with red areas indicating values used in fitting probability distribution tail (units: days and m3/s)
The log-log probability distribution with red dots indicating fitting range and blue line showing the linear fit and indicating power law behaviour, the line indicates an exponent qD =3.03.
Outputs of the function PD
Power Spectrum with red fit performed on the high frequencies between the red stars and with the blue fit performed for low frequencies between the blue stars (for UcheeCreek) absolute logarithmic slopes high frequency (red) b = 1.86, low frequencies b = 0.47.
The function HspecAuto
Logarithmic plot showing scaling behaviour of double trace moments for UcheeCreek. Black stars mark fitting range. l =213 corresponds to one day.
Logarithmic plot of slopes of Figure 8 as functions of η. Blue stars mark fitting range for linear fit, black star marks η0
Outputs from DTMspec
Log-linear graph showing projected extreme values Q (in m3/s) as a function of their return period T (in years, a logarithmic plot)for Uchee Creek (dotted line) along with the actual data (circles). The theory and data are very close giving confidence in the projection.
The principle software used in phases 1A, 1B, 1C now exist in MATLAB code. They have been documented and tested on real streamflow series. Users can now use daily streamflow data to make their own projections for 1000 year return period streamflows.
Recommendation: complete the projectas planned
Phase 2: Analysis of precipitation data with extremes and comparison with streamflow data.
Phase 3: Study of streamflows with strong annual cycles and development of a stochastic model.
Phase 4b: The development and documentation of MATLAB software needed in the remaining phases. The development of maps showing the distribution of exponents, parameters.