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Temperature and Precipitation Projections for the Mobile Bay Region

Appendix

Indicator Definitions

Secondary climate change indicators requested for the greater Mobile Bay region. Unless otherwise indicated, all values are calculated individually for each weather station, for 1980-2009 using both observations and historical simulations, and for the periods 2010-2039, 2040-2069 and 2070-2099 using future simulations.

1. Timeseries of annual average precipitation, maximum, mean, and minimum temperature from 1960 to 2099.

2. Monthly 30-year mean of precipitation, maximum, mean, and minimum temperature

3. Seasonal 30-year mean of precipitation, maximum, mean, and minimum temperature

4. Annual 30-year mean of precipitation, maximum, mean, and minimum temperature

5. Seasonal and annual 30-year average number of days and maximum number of consecutive days with maximum daily temperature >=95F, >100F,105F,110F

6. Annual 30-year mean of 4 consecutive warmest days in summer and coldest days in winter: 5th, 25th, 50th ,75th, 95th percentile

7. Annual coldest day and maximum 7-day average temperature with the % probability (1,5,10,50) of occurrence during 30-year period

8. Annual precipitation for 24-h period with a 0.2, 1, 2, 5, 10, 20, 50 % occurrence during 30-year period

9. Annual two and four-day exceedance probability across 2 consecutive days :0,2, 1,2, 5, 10, 20, 50 percentile and mean (note that these are calculated differently than the variable in #8 above).

10. Seasonal 30-year mean of largest 3-day total precipitation in each season

Dealing with Low-Frequency Quantiles

For certain variables that are sampling beyond the range of the observed historical distribution (e.g., #8 and 9), the 0.2% and 1% exceedences are identical. This is because the distributions are only based on 30 values for each period. On average, creating a distribution from only 30 points means that there will only be one value above 95% and below 5%. So anything above 95% or below 5% is not robust, as this requires extrapolating far beyond the original data used to create the distribution.

The function used here to fit quantiles uses an empirical distribution based on the data, not a theoretical distribution. More information on this routine can be found here: http://stat.ethz.ch/R-manual/R-devel/library/stats/html/quantile.html

However, engineers often use a Log-Pearson distribution to fit precipitation curves. This distribution is theoretical rather than empirical, which means it can extrapolate beyond the ranges of the data used to derive the distribution. For that reason, we asked: what difference would it make if a Log-Pearson fit were used to calculate the quantiles of the distribution?

For the quantiles contained within the range of the data, an empirical distribution is more accurate than fitting a theoretical distribution because it makes no assumptions regarding the distribution of the data. For these quantiles, differences between the two approaches would be a function of how well the theoretical distribution fit the empirical distribution.

For quantiles that lie beyond the range of the data (for example, the 1st or 99th quantiles in a dataset that is made up of less than 99 data points), there is a significant difference between the two approaches. An empirical approach simply assigns an out-of-range quantile the most extreme value on that side of the distribution. So, for example, if the highest value in a distribution of 20 points were 42.5 then the value of 90th quantile and any higher quantile would all be set to 42.5. This method provides a highly constrained estimate of extreme values as it does not allow estimates beyond the range of the data used to derive the distribution. A theoretical distribution, on the other hand, provides some estimate of the shape of the tail beyond the values used to make the distribution. Quantile values outside the range of the data points can then be estimated based on that distribution. Using a theoretical distribution therefore provides an extended estimate of extreme values as it permits estimates beyond the range of observed (or modeled) data.

Since the empirical approach was used to derive the quantiles in this analysis, they should be viewed as minimum estimates for these values. In reality, the values of quantiles beyond the range of the observations used to derive the distribution will be more extreme than the values given here.

Indicator Robustness

Concerns about the robustness of multiple variables were addressed by re-defining certain precipitation variables so as to sample from a greater part of the distribution. This analysis found that:

1. Any difference between the 3 scenarios is insignificant so averaging across all scenarios for precipitation extremes is recommended if the calculations sample from only 30 points.
2. General trends (or lack thereof) appear relatively robust for variable #7.

The "general drop-off" in precipitation towards the end of the century originates directly from the projections from global climate models. Maps showing projected precipitation changes across the entire Southeast have been added to this report to place projections for the Mobile Bay area into the context of the larger geographic context. The general trends are for a decrease in summer precipitation balanced by an increase in fall and winter. Decreases become slightly stronger under higher emissions (annual average changes for A1fi: -6%, A2: -3%) compared to lower (annual average changes for B1: +2%).

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Updated: 3/27/2014
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