Projecting Changes in Extreme Precipitation in the Midwestern United States Using North American Regional Climate Change Assessment Program (NARCCAP) Regional Climate Models

Understanding greenhouse gas sources, emissions, measurements, and management is essential for capture, utilization, reduction, and storage of greenhouse gas, which plays a crucial role in issues such as global warming and climate change. Taking advantage of the authors' experience in greenhouse gases, this book discusses an overview of recently developed techniques, methods, and strategies: - A comprehensive source investigation of greenhouse gases that are emitted from hydrocarbon reservoirs, vehicle transportation, agricultural landscapes, farms, non-cattle confined buildings, and so on. - Recently developed detection and measurement techniques and methods such as photoacoustic spectroscopy, landfill-based carbon dioxide and methane measurement, and miniaturized mass spectrometer.


The Midwestern Region
The definition of the Midwestern region of the USA differs in literature. The Midwestern U.S. defined for the National Climate Change Assessment program (Easterling and Karl, 2000) includes the upper eight states south of the Great Lakes ( Figure 1). We expanded the region to include Kentucky because of its similarities in both physical and socio-economic characters to the rest of the region. Based on 2010 census, the nine states contain about 21% of the nation's population. Their cumulative gross state product is approximately 20% of national gross domestic product of 2010. Therefore it is an area of great economic importance. Situated at the heart of the Corn Belt, the region's economy is dominated by farming, with 89% of the land area being used for agricultural purposes. As a result, climate variability and extreme weather play a key role in the economic productivity of the region. In recent decades, the Midwest region has observed a noticeable increase in average temperatures despite the strong year-to-year variations (Union of Concerned Scientists, 2009). The largest increase has occurred in winter. Both summer and winter precipitation has been above average for the last three decades, making it the wettest period in a century. Heavy rainfall events are also significantly more frequent than a century ago. The Midwest has experienced two record-breaking floods in the past 15 years (Union of Concerned Scientists, 2009). It can be seen from these already observed changes that climate change will have a profound impact on the region. As a result it is very important to investigate how precipitation pattern will change for the region in the near future.
The Midwestern region has a typical continental climate, although the Great Lakes have a great influence on nearby areas for both temperature and precipitation. The total annual precipitation of the region averages at 950 mm . In fall and winter, the precipitation is largely produced by mid-latitude wave cyclones. In spring and summer, it is dominated by varying amount of convective thunderstorm rainfall. In most part of the region, precipitation is highly seasonal, with most of the rainfall concentrated in spring and summer. However in the Ohio River Valley in the southeastern part of the region, the amount of precipitation is fairly constant throughout the year. Spatially, annual precipitation ranges from 600 mm in northwest to 1200 mm in southeast, because of the increasing proximity to the Gulf of Mexico source of moisture ( Figure 1). The slight deviation to this precipitation gradient is leeway shores of the Great Lakes, where lake effect precipitation, particularly from August to December, generates relatively wet conditions that lead to an annual precipitation depth around 900 -1000 mm (Huff and Angel, 1992). Most of extreme precipitation events occur in spring and summer. Heavy precipitation in spring, when evaporation is relatively low due to lower temperature, can lead to severe flooding.
Projecting Changes in Extreme Precipitation in the Midwestern United States Using North American Regional Climate Change Assessment Program (NARCCAP) Regional Climate Models

Data
For model evaluation, observed daily precipitation data 1971-2000 were obtained from US Historical Climatology Network (USHCN) for climate stations in the Midwest Region. The time period was selected because it was the temporal domain of retrospective runs carried out by NARCCAP RCMs. We excluded years with less than 350 days of records to preserve frequency distribution of the data series, and any station with less than 25 complete years of records. We finally had 204 stations, with an average of 28.5 complete years of record per station.
NARCCAP includes 6 RCMs driven by 4 GCMs over the domain of North America, and they typically have the spatial resolution of 50 km. Not all simulations are completed. At the time of this study, 6 of the 24 RCM-GCM combinations are finished and data distributed. Table 1 shows the RCM-GCM combinations used in this study. For model evaluation, we used RCM retrospective runs , which produce 3-hourly precipitation data series. This data was summarized into daily precipitation data series 1971-2000. For projecting future precipitation patterns, we summarized RCM output for 2040-2070 into future daily precipitation data series. All model runs are driven with A2 emission scenario defined by the Intergovernmental Panel on Climate Change (IPCC) Special Report on Emission Scenarios (SRES) (IPCC, 2000). A2 assumes a medium high level of CO 2 emission based on a development pattern close to business-as-usual.

RCMs
GCMs CCSM CGCM3 GFDL HADCM3 CRCM X X MM5I X HRM3 X RCM3 X WRFG X Table 1. GCM-RCM combinations used in this study

Model evaluation methodology
In order to examine the frequency and magnitude of extreme events, it is important for a model to capture an accurate distribution of the data series. We first computed and compared the statistics that describe the shape of distribution for observed and modeled daily precipitation data. We chose to use L-moments to characterize the frequency distributions based on methods developed in Hosking (1990). L-moments are similar to conventional moments in that they are calculated to summarize the shape of a probability distribution. L-mean is identical to the conventional mean, whereas L-scale, L-skewness and L-kurtosis are analogous to conventional standard deviation, skewness and kurtosis. Lmoments however are often considered superior to conventional moments in characterizing distribution shapes, because they are less sensitive to outliers (Ulrych et. al, 2000, Elamir et.al, 2003, and Hosking 2006.
We then attempted to quantify the deviation of the distributions of daily data output from 6 NARCCAP RCMs from observed daily precipitation distribution based on the following steps:  Establish the empirical cumulative distribution function (F obs ) for observed precipitation series for each station: Where 1{A} is the indicator function of event A.  Based on F obs , calculate the probability (p) for each observed precipitation value P j Find the corresponding value in the modeled daily precipitation data for the grid point closest to that station (P j m ) that has the same probability. That is, calculate the quantile (Q m )value at p in the modeled precipitation data series Where n m is the number of data points in the modeled precipitation data series; x m is the sorted modeled precipitation data series where 1 x ;⎾⏋is the ceiling function.


Calculate the model error (E) for each station as the root mean squared difference between P j and P j m Based this method, we evaluated E for complete precipitation data series, as well as the error for observed dry days (E d ) and wet days (E w ) separately at each climate station. We then calculated the mean error for all stations in the state for each model.

Method for projecting future mean and extreme precipitation
A Common approach to studying extreme events is to establish their probability distributions, upon which the magnitude and return intervals (frequency) of extreme events can be established. This can be achieved either by fitting a theoretical distribution functions, or based on the empirical distribution of the data. The advantage of using theoretical distributions is that they can smooth out outliers, particularly when data is only available for short time frame, and they can project beyond the time period when data is available.
Before we can apply this approach, however, we need to correct biases of RCMs in the frequency distribution of their output daily precipitation data series (as evaluated based on the methods outlined in 3.2). It is important to correct the entire distribution, not just mean values. We propose a quantile mapping method to achieve this correction.

Bias correction through quantile mapping
This involves the following steps:  Establish an empirical cumulative distribution function (F mf )for modeled future daily precipitation data series mf For each modeled future precipitation value mf j P , find the corresponding quantile values of same probability in the observed and modeled current daily precipitation data series: obs j P and mc Where n obs is the number of data points in the observed precipitation data series; x obs is the sorted observed precipitation data series where 1 Based on this bias-correction, we derived a future daily precipitation data series from RCMs for each of the climate station.

Frequency analysis
After the bias in the distribution is corrected, we then fit a theoretical distribution function to both the observed and future modeled data, based on which the magnitude of precipitation events of certain return intervals can be established for comparison. A variety of distribution functions have been used to study extreme precipitation events, such as generalized extreme value (GEV), Weibull and Pearson III distributions for annual maxima data, generalized Pareto (GP) distribution for excesses over a high threshold, and generalized Logistic (GL), lognormal (LN) and Gamma distributions for full precipitation records. We used the L-moment ratio (L-skewness vs. L-kurtosis) diagram (Rao and Hamed, 1999) to help select the best distribution for our data. Figure 2 plot the L-skewness and Lkurtosis ratios for both observed and modeled data for all stations. Results show that Gamma distribution best approximate the distribution of daily precipitation totals. This selection is also supported by many previous studies (Crutcher et al. 1977, Buishand 1978, Guttman et al. 1993, Groisman et al. 1999. Gamma distribution has the following density function: The variable x has lower bound of zero, 0< x < ∞. For this family of distributions, theparameter defines the shape of the distribution, while -parameter characterizes the scale. Since it does not rain every day, a mixed distribution model is sometimes considered for daily precipitation totals (Groisman et al, 1999). Under this model, it is assumed that the occurrence of daily precipitation events has a binary distribution with the probability of a single event p pr , and the precipitation amount during this event is considered to have a gamma-distribution. The cumulative distribution function of precipitation totals F(x) is expressed as: with f(α,β,t)dt being the probability density function of gamma-distribution. p pr can be estimated as the percentage of wet days in the data series. The maximum likelihood method is used to estimate the parameters and for each of the observed and future modeled www.intechopen.com Projecting Changes in Extreme Precipitation in the Midwestern United States Using North American Regional Climate Change Assessment Program (NARCCAP) Regional Climate Models 343 daily precipitation data series. After the cumulative probably density function F(x) is established we can derive the magnitude of precipitation events of various return intervals as: Where P y is the precipitation value with the return interval of y years, F -1 (x) is the inverse function of the cumulative probability function F(x).

Model evaluation: Frequency distributions of observed and modeled daily precipitation data
Summary L-moment statistics for frequency distributions of observed and modeled daily precipitation data series are presented in Table 2. It can be seen that CCSM_WRFG daily precipitation series deviate most from the observed distribution of daily precipitation. The remaining models have comparable biases. They all have greater mean (except for CCSM_MM5I), less variance, skewness and kurtosis. This seems to indicate that the modeled data is less spread out, have higher values in small precipitation events and lower values in large events (hence less skewed than observed). It should be noted that to evaluate a model's performance at estimating mean precipitation, we should not only look at the correlation coefficient, but also how closely the points follow the x=y line. It can be seen that CCSM_WRFG model consistently under-estimate the mean daily precipitation. Most models slightly over estimate the mean daily precipitation (such as CGCM_RCM3, GFDL_RCM3 and HADCM3_HRM3). The model that performs best in terms of mean precipitation is CGCM3_CRCM, which has the highest correlation coefficient (0.81), and follows x=y line most closely. However, close estimate in mean precipitation does not mean the model also simulates well the whole distribution of daily precipitation data series. Figure 4 presents the quantile-quantile (Q-Q) plots between observed and modeled data for all stations for each of the 6 RCMs in order to show the deviation from observed distribution as well as the spread of different models. It can be seen from figure 4 that despite its close estimate of mean precipitation, CGCM3_CRCM performs the worst in estimating the complete distribution. It consistently underestimates most of the wet day quantile values. The close estimate of the mean is a result of over-estimation of small precipitation events offsetting this underestimation of larger quantile values. Figure 4 shows that majority of models underestimate large quantile values. All models overestimate days with no or small amount of precipitation. This can also be illustrated by the dry day quintile errors (E d ) presented in table 3. To some extent, this could be attributable to the fact that RCMs output average precipitation of a whole grid, which covers an area of 50 by 50 km, whereas station data are point-based. Table 3 summarizes root mean squared error of modeled quantile values for all data (E), dry days (E d ) and wet days (E w ) respectively. Based on RMSE, it seems that HADCM3_HRM3 performs best in estimating the observed frequency distribution of daily precipitation data, as it has lowest E and E w , and fairly low E d . The calculated model errors again confirm that CCSM_WRFG and CGCM3_CRCM have the poorest performance in simulating the frequency distribution, and its model errors are above the other models. The rest of the models have comparable performance. The average RMSE for full record quantiles for all models is about 1 mm, or about 40% of mean precipitation amount. This ranges from 0.78 to 1.65 mm, or 30 to 63% of mean daily precipitation. The average RMSE for wet day quantile values for all models is 3.04 mm, or 35% of the mean wet day precipitation. It ranges between 25-54% of mean wet day precipitation among different models.
Projecting Changes in Extreme Precipitation in the Midwestern United States Using North American Regional Climate Change Assessment Program (NARCCAP) Regional Climate Models

Mean daily precipitation
After applying bias correction based on quantile mapping method, we calculated future mean daily precipitation for the Midwest region for the time period 2040-2070. Table 4 summarizes how daily mean precipitation might change for the study area based on climate models. With the exception of CCSM_WRFG (which projects very slight decrease), all other models project increase in mean precipitation in the region. The average change for all models is 7.7%, ranging from 0-12%. Figure 5 shows the spatial pattern of precipitation change based on mean projection of all models. It seems that mean precipitation is likely to increase more in north and less in the south. This is likely due to increased evaporation from the Great Lakes under a warmer temperature. Spatial pattern of mean precipitation change varies among different models ( Figure 6), but most models project increase in the northern part of the region. CCSM_WRFG is the only model that project decrease of precipitation in the south at the similar magnitude as the increase in the north. All other models project increase in all Midwest region.  www.intechopen.com more for more extreme events. Similar to the pattern of mean precipitation change, there seems to be more increase in extreme events in the northern part of the region. Since a lot of extreme precipitation events occur in spring, this increase could be attributed to decreased ice cover during the winter, early melt of lake ice, and consequent increased evaporation of the great lakes under a warmer climate.

Conclusion
In this study, we first evaluated the performance of NARCCAP regional climate models in terms of its ability to capture the frequency distribution of daily precipitation data in the Midwest region of the United States. We found all models have biases. In general, they tend to overestimate small events, and underestimate large events. Based on such evaluation, we corrected model biases based on quantile-mapping method. We then used the bias-corrected future daily precipitation output from NARCCAP RCMs to project future changes in precipitation using a mixed probability model based on Gamma distribution. Based on the models, on average, the mean precipitation could increase by 7.7% by 2040-2070 for the Midwestern Region. Magnitudes of extreme precipitation are likely to increase more than average. The increase could be disproportionately larger for more extreme precipitation events. Spatially, northern part of the study area could see more increase in both mean and extreme precipitation, likely due to increased evaporation of the Great Lakes from a combination of higher temperature and less ice cover both spatially and temporally under a warmer climate.