Energy2green Wind And Solar Power System

To examine the hurricane-sun relationship in more detail we consider daily data. We first spline interpolate the 6-hr positions and maximum wind speeds to hourly values (Jagger and Elsner 2006) using the U.S. National Hurricane Center besttrack data (Neumann et al. 1999) for all tropical storms and hurricanes over the 63-year period 1944-2006. Tropical cyclones over the Caribbean Sea and near the United States were routinely monitored with aircraft reconnaissance during this time period. We then compute daily average tropical cyclone wind speed intensity from the spline-interpolated values.

Tropical cyclone intensity depends on many factors including low-level spin and wind shear. These factors will confound attempts to identify a solar signal in the data. In order to provide some control, we correlate tropical cyclone intensity with solar activity using cyclones over a uniformly warm part of the western half of the basin and mainly within the deep tropics. The domain is bounded by 65 and 100 degrees W longitude and 10 and 30 degrees N latitude (Fig. 2a). This region is where oceanic heat content is the largest during the hurricane season so the limiting thermodynamic variable is upper atmosphere temperature rather than SST.

The rank correlation between daily SSN and daily averaged tropical cyclone intensity for all tropical storms and hurricanes in the domain over the period 19442006 is —0.11 (p value < 0.001,413 dof). Although explaining only a small amount of the variability, the result is consistent with output from the seasonal models above showing an inverse relationship between hurricane intensity and solar activity. The daily correlation between SSN and storm intensity is based on the Spearman rank correlation since daily SSN and tropical cyclone intensity are not multivariate normal. The significance includes a reduction in the degrees of freedom since daily intensities and SSN are serially correlated. Each storm is given one degree of freedom regardless of the number of days it stays in the region.

Fig. 2 Region map and upper quantiles of hurricane intensity grouped by daily sunspot numbers. a. Solid boxes delineate regions used to model daily tropical cyclone intensities. The dotted box delineates the averaging region for SST as an index of ocean heat content for the seasonal model of tropical cyclone activity. b. Quantile values and regression model lines using daily tropical cyclone intensity in the western basin as the response and daily SSN as the covariate. The symbols correspond to the 50th, 75th, 90th, 95th, and 99th percentiles starting at the bottom for each sunspot group. The lines correspond to the respective quantile regression lines. Numbers above the abscissa are the sample sizes (number of days with sunspot numbers in the interval). c. Same as b, except for the eastern Atlantic basin

Fig. 2 Region map and upper quantiles of hurricane intensity grouped by daily sunspot numbers. a. Solid boxes delineate regions used to model daily tropical cyclone intensities. The dotted box delineates the averaging region for SST as an index of ocean heat content for the seasonal model of tropical cyclone activity. b. Quantile values and regression model lines using daily tropical cyclone intensity in the western basin as the response and daily SSN as the covariate. The symbols correspond to the 50th, 75th, 90th, 95th, and 99th percentiles starting at the bottom for each sunspot group. The lines correspond to the respective quantile regression lines. Numbers above the abscissa are the sample sizes (number of days with sunspot numbers in the interval). c. Same as b, except for the eastern Atlantic basin

Quantile regression is a model to estimate the conditional quantile of a response variable given a set of observed covariates. Here we consider the 50, 75, 90, 95 and 99 percentiles of daily mean maximum tropical cyclone wind speed as an affine transformation of the daily number of sunspots. Quantile regression is an extension of median regression based on estimating the value of the parameter vector from the set of allowable vectors that minimizes the mean loss function

where the y's are the response values, mu is the estimate of the tau quantile, and the x's and beta's are the covariate vector and parameter vector, respectively. The loss function is p sub tau, where pt(z) = |z|{t • I(z > 0) + (1 - t) • I(z < 0)}

and I(x) is the indicator function, which is one when x is true and zero otherwise. The loss function is non-negative taking a minimum value of zero only when z is zero.

If one has a series of samples and mu is a constant, i.e. an intercept-only model, then the resulting value of beta that minimizes the total loss function occurs only when mu is equal to the tau quantile of the response. Then, if the model fits well, a plot of the fitted values versus the actual values will show that tau observed values are less than the fitted values, with 1-tau observed values greater than the fitted values (Yu et al. 2003). The total loss function is an unbiased sample estimate of the expected value of

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