## Thursday, August 28, 2014

## Sunday, August 17, 2014

### Heavy Rainfall Trends in the U.S.

Significant research has been conducted in recent years regarding changes in precipitation amounts and patterns in a warming climate. From a theoretical perspective, warmer air holds more moisture so increases in temperature should lead to increases in precipitation. On the flip side, increased temperatures may dry out soils and lakes (sources of moisture), cause air currents to change, or lead to other situations that counter-balance the increase in atmospheric moisture.

A chapter from the recently released National Climate Assessment discusses the trends in long-term heavy precipitation events for the entire U.S. during the last century. In particular, they note how the proportion of annual precipitation from extreme events has increased since the 1950's. The map below shows Figure 2.18 from that report. The map shows that large increases in very heavy precipitation events have been observed in the eastern half of the country.

I am interested in knowing how the rate of heavy precipitation events has changed at smaller geographical scales. Therefore, I decided to look at all airport stations in the U.S. that have a continuous record dating back multiple decades. In this instance, a beginning point of 1949 was chosen because 207 stations have complete precipitation records between 1949 and 2013 (additional stations with 1 or 2 missing months during the same time period will be added at a future date). This is also a long enough period of time to smooth out increases or decreases due to cyclical climate oscillations with short (<10 year) periods. Cooperative stations were excluded since the time of observation is not consistent from one station to the next and in some cases it changes intra-annually at single stations. Therefore, only airport stations with midnight-to-midnight reporting times were used.

The 207 stations are nicely distributed geographically with a slightly higher density east of the Rocky Mountains and a lower density west of the Rocky Mountain Front Range. The following map (Figure 2) shows the distribution of stations.

For the purpose of this analysis, we are not studying the temporal spread of singular heavy rain events – just the frequency of high precipitation events. In fact, the year with the highest precipitation event for the 1949-2013 time period at each station is not statistically significant when grouping the years into eight categories. Figure 3 shows the year range of the highest precipitation event for each of the 207 stations. There is a slight tendency for the records to be more frequent in recent years but the significance level (

Figure 3. Year when highest calendar day precipitation event for all stations during the 1949-2013 time period was recorded.

Figure 4. Number of maximum precipitation events grouped by year of occurrence for all 207 stations during the 1949-2013 time period.

For each station, a linear regression line was fitted to the number of days per year that met or exceeded A) 0.05", B) 0.50", C) 1.00", D) 2.00", and E) 3.00". The first value (0.05") was chosen as a proxy measure for the overall number of rainfall events per year. A smaller value was not used so that future research can extend the analysis to Cooperative stations. Those stations, especially early in their climate records, missed some small precipitation events. The 0.05" value allows us to determine if all precipitation events are increasing or decreasing – not just heavy events.

Once a linear regression was completed for each station at each of the four precipitation thresholds, a probability value (

As an example, the Dallas Fort Worth International Airport (GHCN ID: USW00003927) saw a slight decrease in number of days with at least 0.05" of precipitation between 1949 and 2013. However, the

Instead of plotting percent change (or raw value change) for each station from 1949-2013, I decided to plot statistical significance – using the aforementioned

Most of the stations in the U.S. experienced no statistically significant increase or decrease in the number of days with at least 0.05" of precipitation. A band of stations from the Dakotas to the eastern Great Lakes saw statistically significant increases and some areas in the Southeast saw statistically significant decreases but most of the U.S. was nondescript.

Using a threshold of 0.50", patterns begin to emerge. Many stations from northern Texas to the Dakotas and then eastward to include the entirely of New England saw a statistically significant increase in the number of days with at least 0.50" of precipitation. Much of the West consistently recorded a decrease in the number of days with 0.50" of precipitation but only a few stations were statistically significant.

The statistical significance pattern is even more apparent when looking at days with at least 1.00" of precipitation. Nearly 90% of stations east of the Rocky Mountains saw an increase in the number of 1.00" precipitation days and approximately half of those stations met the 95% statistical significance threshold. Notice that some stations in the Intermountain West receive too few days per year (<0.5) to be included in the analysis.

At the 2.00" threshold, the trend direction (positive or negative) and the significance levels are not nearly as distinct as they were for the 0.50" and 1.00" events. Nevertheless, a clear pattern exists in the northeastern portion of the country and a strong majority of stations east of the Rocky Mountains saw an increase in the number of days with at least 2.00" of precipitation. West of the Rocky Mountain Front Range, a majority of stations (65) receive too few days per year to make meaningful assessments.

Figure 8. Significance map of trend in number of days with 2.00" of precipitation or greater during the 1949-2013 time period.

At the 3.00" threshold, only 61 stations had the requisite number of days per year (0.5) of events to qualify for significance analysis. The stations that met the minimum requirements run from eastern Texas northward to the Oklahoma-Kansas boundary and then northeastward to southern New England. of the 61 stations, 43 were in one of the

Figure 9. Significance map of trend in number of days with 3.00" of precipitation or greater during the 1949-2013 time period.

The primary purpose of this analysis was to assess changes in the frequency of heavy precipitation events in small geographical units. That being said, it is helpful to look at the results when all stations are averaged together. To do this, every station had an average value computed representing the average number of days with at least a certain amount of precipitation (e.g., >=0.05"). Then the value for each year was compared against that average and a percentage above or below the average value was recorded. If, for example, a station averaged 80 days per year with at least 0.05" of precipitation, a year with 88 days would be recorded as 110% of the average. This averaging technique was performed for all station, in all years, for each precipitation threshold. Using percentages prevents stations with large numbers of precipitation days (e.g., New Orleans) from overwhelming stations with small numbers of days (e.g., Las Vegas). Figure 10 shows the number of days per year with at least 1.00" of precipitation between 1949 and 2013 as an example of the spatial variability in heavy rainfall events.

Figure 10. Average number of days with 1.00" of precipitation or greater during the 1949-2013 time period.

As you can see, stations in the southeastern corner of the U.S. have far more days per year with at least 1.00" of precipitation. If, for example, the number of days in Mobile, AL, and Salt Lake City, UT, both increased by 2 days per year, using raw numbers masks the change in Salt Lake City whereas using percentages does not. Therefore, any methodology that does not normalize the data runs the risk of being a

The change in the number of days per year with at least 0.05" is pretty chaotic across the entire U.S. There are long periods with consistently upward or downward trends but overall the values are pretty flat. Beginning in 1998, the rate of change dropped noticeably. This also corresponds to period of record or near record worldwide temperatures. The

The nationwide change in the number of days per year with at least 0.50" consistently increased for most of the 65 year analysis period. As with the 0.05" chart, the rate of change dropped in 1998. The

The change in the number of days per year with at least 1.00" was strongly positive. The increase in the number of days per year is greater than 10% and the post-1998 deviations from the prior two charts are just 1 or 2 year anomalies on the 1.00" chart. In fact, the

The change in the number of days per year with at least 2.00" was even more strongly positive. The

Figure 14. Annual average of each station's percentage from the long-term average number of days with at least 2.00" of precipitation.

The change in the number of days per year with at least 3.00" was strongly positive, but less than the 2.00" threshold. The

Figure 15. Annual average of each station's percentage from the long-term average number of days with at least 3.00" of precipitation.

We showed that the rate of small precipitation events has not changed much in the last 64 years (see Figure 5). However, when the precipitation intensity rises, the strength of the statistical significance rises. Most of the eastern half of the U.S. has experienced an increase in the number of days with at least 0.50", 1.00", 2.00", and 3.00" of precipitation. The western half of the country has, on average, seen a slight decline in the rate of those precipitation thresholds when enough observations are available for analysis– but not at a statistically significant level.

At the station level, the long-term trend of days at different intensity thresholds tells a more complete story than just looking at regional data using state boundaries. While data at an individual station is not sufficient to draw very many conclusions, aggregating station data in this manner allows us to draw new conclusions about how precipitation patterns change over space and time.

A complete list of the stations used in the analysis can be found Here.

A chapter from the recently released National Climate Assessment discusses the trends in long-term heavy precipitation events for the entire U.S. during the last century. In particular, they note how the proportion of annual precipitation from extreme events has increased since the 1950's. The map below shows Figure 2.18 from that report. The map shows that large increases in very heavy precipitation events have been observed in the eastern half of the country.

Figure 1. Map from National Climate Assessment (Figure 2.18) showing the observed change in heavy precipitation events.

I am interested in knowing how the rate of heavy precipitation events has changed at smaller geographical scales. Therefore, I decided to look at all airport stations in the U.S. that have a continuous record dating back multiple decades. In this instance, a beginning point of 1949 was chosen because 207 stations have complete precipitation records between 1949 and 2013 (additional stations with 1 or 2 missing months during the same time period will be added at a future date). This is also a long enough period of time to smooth out increases or decreases due to cyclical climate oscillations with short (<10 year) periods. Cooperative stations were excluded since the time of observation is not consistent from one station to the next and in some cases it changes intra-annually at single stations. Therefore, only airport stations with midnight-to-midnight reporting times were used.

The 207 stations are nicely distributed geographically with a slightly higher density east of the Rocky Mountains and a lower density west of the Rocky Mountain Front Range. The following map (Figure 2) shows the distribution of stations.

Figure 2. Locations of airport stations with complete precipitation data from 1949-2013. A total of 207 stations met the criteria.

For the purpose of this analysis, we are not studying the temporal spread of singular heavy rain events – just the frequency of high precipitation events. In fact, the year with the highest precipitation event for the 1949-2013 time period at each station is not statistically significant when grouping the years into eight categories. Figure 3 shows the year range of the highest precipitation event for each of the 207 stations. There is a slight tendency for the records to be more frequent in recent years but the significance level (

*p*-value) is only 0.15 and is therefore not significant at the 95% or 90% level. If there was an 85% significance category it would fall within that bound (See Figure 4).Figure 4. Number of maximum precipitation events grouped by year of occurrence for all 207 stations during the 1949-2013 time period.

*Methodology*For each station, a linear regression line was fitted to the number of days per year that met or exceeded A) 0.05", B) 0.50", C) 1.00", D) 2.00", and E) 3.00". The first value (0.05") was chosen as a proxy measure for the overall number of rainfall events per year. A smaller value was not used so that future research can extend the analysis to Cooperative stations. Those stations, especially early in their climate records, missed some small precipitation events. The 0.05" value allows us to determine if all precipitation events are increasing or decreasing – not just heavy events.

Once a linear regression was completed for each station at each of the four precipitation thresholds, a probability value (

*p*-value) was computed. The*p*-value is a statistical measure of significance. A*p*-value less than 0.05 indicates that there is a less than 5% chance that the statistical trend is random. A*p*-value less than 0.10 indicates that there is a less than 10% chance that the statistical trend is random. By convention, a*p*-value greater than 0.10 is considered not statistically significant.As an example, the Dallas Fort Worth International Airport (GHCN ID: USW00003927) saw a slight decrease in number of days with at least 0.05" of precipitation between 1949 and 2013. However, the

*p*-value was 0.93 – indicating near total randomness in the distribution. Looking at the number of days with at least 0.50", there was an increase over time and the*p*-value was 0.045. Since this number is less than 0.05, the upward trend is considered significant at the 95% level. The*p*-value for the trend in days with at least 1.00" was 0.16, for days with at least 2.00" was 0.70, and for days with at least 3.00" was 0.42 – all not significant at the 95% or 90% levels. Collectively, we conclude that the Dallas Fort Worth International Airport has observed a statistically significant increase in the number of days with at least 0.50" of precipitation but all other thresholds were not significant.*Statistical Significance Maps*Instead of plotting percent change (or raw value change) for each station from 1949-2013, I decided to plot statistical significance – using the aforementioned

*p*-value. For example, if a station showed at 20% increase in the number of days with 1.00" or more between 1949 and 2013, 1 or 2 years might be responsible for all of the increase. Therefore, the increase, in that example, is an aberration and not an actual trend. However, we can compute a statistical significance for that station's trend line and report back whether or not the 20% increase was meaningful at the 95% or 90% significance level. For all of the statistical significance calculations and maps, a station must have an average at least 0.5 days per year to calculate a trend – otherwise they are identified as "too few events."*Days per year with at least 0.05"*
Figure 5. Significance map of trend in number of days with 0.05" of precipitation or greater during the 1949-2013 time period.

*Days per year with at least 0.50"*Using a threshold of 0.50", patterns begin to emerge. Many stations from northern Texas to the Dakotas and then eastward to include the entirely of New England saw a statistically significant increase in the number of days with at least 0.50" of precipitation. Much of the West consistently recorded a decrease in the number of days with 0.50" of precipitation but only a few stations were statistically significant.

Figure 6. Significance map of trend in number of days with 0.50" of precipitation or greater during the 1949-2013 time period.

*Days per year with at least 1.00"*The statistical significance pattern is even more apparent when looking at days with at least 1.00" of precipitation. Nearly 90% of stations east of the Rocky Mountains saw an increase in the number of 1.00" precipitation days and approximately half of those stations met the 95% statistical significance threshold. Notice that some stations in the Intermountain West receive too few days per year (<0.5) to be included in the analysis.

Figure 7. Significance map of trend in number of days with 1.00" of precipitation or greater during the 1949-2013 time period.

*Days per year with at least 2.00"*At the 2.00" threshold, the trend direction (positive or negative) and the significance levels are not nearly as distinct as they were for the 0.50" and 1.00" events. Nevertheless, a clear pattern exists in the northeastern portion of the country and a strong majority of stations east of the Rocky Mountains saw an increase in the number of days with at least 2.00" of precipitation. West of the Rocky Mountain Front Range, a majority of stations (65) receive too few days per year to make meaningful assessments.

*Days per year with at least 3.00"*At the 3.00" threshold, only 61 stations had the requisite number of days per year (0.5) of events to qualify for significance analysis. The stations that met the minimum requirements run from eastern Texas northward to the Oklahoma-Kansas boundary and then northeastward to southern New England. of the 61 stations, 43 were in one of the

*increase*categories and only 18 were in a*decrease*category.Figure 9. Significance map of trend in number of days with 3.00" of precipitation or greater during the 1949-2013 time period.

*All Stations Averaged Together*The primary purpose of this analysis was to assess changes in the frequency of heavy precipitation events in small geographical units. That being said, it is helpful to look at the results when all stations are averaged together. To do this, every station had an average value computed representing the average number of days with at least a certain amount of precipitation (e.g., >=0.05"). Then the value for each year was compared against that average and a percentage above or below the average value was recorded. If, for example, a station averaged 80 days per year with at least 0.05" of precipitation, a year with 88 days would be recorded as 110% of the average. This averaging technique was performed for all station, in all years, for each precipitation threshold. Using percentages prevents stations with large numbers of precipitation days (e.g., New Orleans) from overwhelming stations with small numbers of days (e.g., Las Vegas). Figure 10 shows the number of days per year with at least 1.00" of precipitation between 1949 and 2013 as an example of the spatial variability in heavy rainfall events.

As you can see, stations in the southeastern corner of the U.S. have far more days per year with at least 1.00" of precipitation. If, for example, the number of days in Mobile, AL, and Salt Lake City, UT, both increased by 2 days per year, using raw numbers masks the change in Salt Lake City whereas using percentages does not. Therefore, any methodology that does not normalize the data runs the risk of being a

*de facto*analysis of only those stations that have large average annual precipitation amounts.*Days per year with at least 0.05"*The change in the number of days per year with at least 0.05" is pretty chaotic across the entire U.S. There are long periods with consistently upward or downward trends but overall the values are pretty flat. Beginning in 1998, the rate of change dropped noticeably. This also corresponds to period of record or near record worldwide temperatures. The

*p*-value of 0.55 indicates that the overall trend is not statistically significant.
Figure 11. Annual average of each station's percentage from the long-term average number of days with at least 0.05" of precipitation.

*Days per year with at least 0.50"*The nationwide change in the number of days per year with at least 0.50" consistently increased for most of the 65 year analysis period. As with the 0.05" chart, the rate of change dropped in 1998. The

*p*-value of 0.004 indicates that the trend is strongly statistically significant at the 95% (and even at the 99%) level over the course of the analysis period.
Figure 12. Annual average of each station's percentage from the long-term average number of days with at least 0.50" of precipitation.

*Days per year with at least 1.00"*The change in the number of days per year with at least 1.00" was strongly positive. The increase in the number of days per year is greater than 10% and the post-1998 deviations from the prior two charts are just 1 or 2 year anomalies on the 1.00" chart. In fact, the

*p*-value of 0.0001 indicates that the trend is statistically significant at the 99% level. All 207 stations were included in this analysis – even the 17 stations that do not average at least 0.5 days per year with 1.00" of precipitation.
Figure 13. Annual average of each station's percentage from the long-term average number of days with at least 1.00" of precipitation.

*Days per year with at least 2.00"*The change in the number of days per year with at least 2.00" was even more strongly positive. The

*p*-value of 0.0008 indicates a very high degree of statistical significance. Since the vast majority of the excluded stations are in the western U.S., this chart essentially reflects the statistical trend of the eastern half of the U.S. only. As Figures 5 and 6 demonstrate, the trends for the eastern half of the U.S. is much more prominent than for the western half. All stations were included in this analysis.Figure 14. Annual average of each station's percentage from the long-term average number of days with at least 2.00" of precipitation.

*Days per year with at least 3.00"*The change in the number of days per year with at least 3.00" was strongly positive, but less than the 2.00" threshold. The

*p*-value of 0.0001 indicates a very high degree of statistical significance. The map for 3.00" trends appears chaotic when looking at individual stations but when aggregated, the trend is unmistakably upward. However, since the stations that experience 3.00" precipitation events are geographically concentrated in approximately 1/4 of the U.S., this should be considered a regional trend.Figure 15. Annual average of each station's percentage from the long-term average number of days with at least 3.00" of precipitation.

*Conclusion*We showed that the rate of small precipitation events has not changed much in the last 64 years (see Figure 5). However, when the precipitation intensity rises, the strength of the statistical significance rises. Most of the eastern half of the U.S. has experienced an increase in the number of days with at least 0.50", 1.00", 2.00", and 3.00" of precipitation. The western half of the country has, on average, seen a slight decline in the rate of those precipitation thresholds when enough observations are available for analysis– but not at a statistically significant level.

At the station level, the long-term trend of days at different intensity thresholds tells a more complete story than just looking at regional data using state boundaries. While data at an individual station is not sufficient to draw very many conclusions, aggregating station data in this manner allows us to draw new conclusions about how precipitation patterns change over space and time.

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