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Long-term precipitation trend as a function of isentropic variability
Atmospheric Environment 45 (2011) 5822e5827
Contents lists available at ScienceDirect
Atmospheric Environment journal homepage: www.elsevier.com/locate/atmosenv
Long-term precipitation trend as a function of isentropic variability Robert C. Balling Jr. a, Kimberly DeBiasse a, Matthew B. Pace a, Randall S. Cerveny a, *, David M. Brommer b a b
School of Geographical Sciences & Urban Planning, Arizona State University, Tempe, AZ 85302-0104, USA Department of Geography, University of Alabama, Tuscaloosa, AL 35487-0322, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 December 2010 Received in revised form 15 June 2011 Accepted 5 July 2011
Analysis of trends in climatological isentropes provides a means of evaluating seasonal precipitation trends. Past research has indicated that isentropic patterns are linked to moisture influx and adiabatic uplift. We calculate trends across the summer 315 K isentropic surface for the conterminous United States over the last fifty years. We identify positive correlations between time and the pressure levels of the 315 K isentropic surface in the southern Plains states and the New England area. Such correlations suggest long-term rising of pressures (lowering heights) for the isentropic surface (and therefore enhanced moisture inflow) into those regions. Weaker correlations with time and the isentropic surface are found in the Southwest and in the Northwest. Using two well-accepted precipitation databases, we compare the map pattern correlations between the trends in isentropic surfaces and the trends in both precipitation daily totals and in hourly durations. A strong correlation (þ0.67) exists between the trends in the isentropic surface and the daily precipitation and indicates that the precipitation increases are likely influenced by a stronger moisture influx. A weaker positive correlation (þ0.44) is evident between the trends in daily precipitation intensity and the trends in the 315 K isentropic surface. However, the spatial relationship between the trends in the isentropic surface and the trends in the hourly precipitation duration is only 0.07 indicating no significant accounting of trends in duration by corresponding isentrope surface trends. Continued study of the relatively neglected analysis of climatological isentropes will add to our understanding of the physical changes in precipitation patterns across the United States. Published by Elsevier Ltd.
Keywords: Isentropic surface Precipitation characteristics Climate change
1. Introduction One key to achieving a complete understanding of climate change is to produce a clear visualization of climate variables (e.g., precipitation) and the climatological processes that influence those variables. However, many atmospheric visualizations, such as upper-air isobaric analyses, are based on utilitarian needs of short-term meteorological operations (e.g., aviation) and were not created to necessarily demonstrate or analyze climatic processes. Isentropic analysis is based on the concept of dry adiabatic warming and cooling of atmospheric parcels through uplift or descent. In isentropic analysis, the analyst computes the pressure level associated with a given potential temperature (q) value, which is the temperature of an air parcel undergoing compression or expansion adiabatically to a pressure of 100 kPa (1000 mb). Given such a definition, a set of potential temperatures can be produced
* Corresponding author. E-mail address: [email protected] (R.S. Cerveny). 1352-2310/$ e see front matter Published by Elsevier Ltd. doi:10.1016/j.atmosenv.2011.07.013
for each rawinsonde sounding, throughout its upward movement. Normally, a specific isentropic temperature (e.g., q ¼ 305 K) is selected and the pressure (or, in early research, the height) corresponding to that isentropic value is plotted across the network of rawinsonde stations. Previous researchers have highlighted the usefulness of climatological isentropic analyses in identifying seasonal moisture and precipitation patterns (Namias, 1940; Cerveny et al., 2011) and longterm drought patterns (Wexler and Namias, 1938; Cerveny et al., 2011). In this study, we focus on how trends and variations in isentropic surfaces are related to trends and variations in characteristics of precipitation. As climatological isentropic research’s originator Jerome Namias and others have stressed, the primary advantage of isentropic analysis is that it “offers the ability to look at atmospheric motion in the way it actually happens e i.e., in three dimensions due to the fact that isentropic surfaces follow the true motion of a parcel” (De Conning, 2000, p. 377). Namias himself noted that the primary functions of the isentropic chart were (1) to facilitate the study of the identification and thermodynamic modification of large-scale air currents, and (2) to present a clear-cut picture of the major patterns of flow of atmospheric currents (Namias, 1940).
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2. Isentropic analysis 2.1. Theory of isentropic analysis The climatological aspects of isentropic analysis, the use and interpretation of atmospheric charts representing surfaces of constant potential temperature, were first introduced as a research tool by Namias in the 1930s. Early researchers maintained that the primary advantage of this analysis was that “. isentropic surfaces . give a much better picture of flow pattern than fixed-level charts and show the dry and moist tongues. This form of analysis allows a much better correlation of rainfall-patterns with upper-air phenomena than was possible [with constant pressure charts] .” (Wexler and Namias, 1938, p. 164). If isentropic patterns are being modified by long-term forcing mechanisms, such as anthropogenic influences and/or solar variability, this would suggest that the moisture and adiabatic uplift regions, and hence precipitation patterns, are also being impacted by that variability. Identification of any changes in uplift regions would be useful to forecasters and water managers. Consequently, we examine the spatial correlation of the trends in seasonal precipitation with changes in the isentropic surface. Potential temperature (q) as derived from one of the three Poisson’s relationships (Holton, 1992), can be expressed as:
R p cp q ¼ T s p
(1)
where T is the ambient temperature (K), ps is a standard reference pressure (100 kPa or 1000 hPa), p is the pressure, R is the gas constant for dry air (287 J K1 kg1), and cp is the specific heat of dry air at constant pressure (1004 J K1 kg1). Potential temperature is the corresponding temperature of a parcel of air moved adiabatically from its original pressure to 100 kPa. Therefore, movement along a constant potential temperature path is an adiabatic process. Although the majority of isentropic analysis since Namias’ work in the 1930s and 1940s has focused on the concepts surrounding isentropic potential vorticity (Hoskins, 1991), we are applying Namias’ original style of climatological isentropic analysis such as the one used in drought depiction and prediction (e.g., Wexler and Namias, 1938; Cerveny et al., 2011). 2.2. Mean isentropic surface Our modern isentropic analyses incorporate data from 1958 to 2010 generated using the raw sounding data from the CD-ROM “Radiosonde Data of North America 1946e1996” with updates to 2010, which is issued by the Forecast Systems Laboratory and National Climatic Data Center (Forecast Systems Laboratory, 1997). Although, traditionally the National Centers for Environmental Prediction
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(NCEP) reanalysis data (Kalnay et al., 1996) have been used for modern climate pattern analyses, those data are constructed on sigma pressure fields and consequently are not suitable for isentropic analysis. We extracted data from sixty long-term (1958e2008) upper-air rawinsonde sites, those stations which had a complete long-term record omitting those with large gaps of missing data. We then applied those data to equation (1) and the resultant potential temperature (isentrope) values to the nearest hectopascal (millibar) were interpolated for the average of the 00 UTC and 12 UTC soundings for the stations across the United States. Wind speed and direction were also interpolated at the various pressure and/or height levels associated with the isentropic surface. For this study, concentrating on the summer season, we selected the 315 K isentropic surface as suggested by Namias (1940) to ensure that the potential temperature surfaces would be above ground level. We calculated the average isentropic pressure for the summer months of June, July, and August (JJA) from all available 00 UTC and 12 UTC rawinsonde measurements over the 1958e2008 study period. Unfortunately, calculation of temporal trends in the isentropic dataset is complicated by the large number of missing months at many of the rawinsonde stations (due to station relocation and, unfortunately, some elimination of stations). We ultimately computed the linear trend in the data for the period 1958e2008 with the criterion that a station must have 40 years of valid continuous data for a given month; the trends were calculated separately for each month and averaged for the summer season. Fig. 1 shows the average pressure level of the summer (JJA) 315 K isentropic surface based on 46 stations of the original 60 stations that met our criteria based on missing data. The surface was produced using universal kriging and the resultant smooth surface explains 94.2 per cent of the spatial variance in the original data. The map depicts the classic monsoonal flow with higher pressure levels (lower heights) for the 315 K surface in the American Southwest. This isentropic trough arcs into the American Great Plains. Such an isentropic pattern, although identified using fewer stations with less temporal coverage, was described as far back in Namias (1940). As Namias (1940) noted, the occurrence of lower elevation/higher pressures of a given isentropic surface corresponds to adiabatic flow of moisture. The existence of this pronounced Southwest moisture tongue has been linked to the influx of moisture from the Gulf of California and Gulf of Mexico and, thereby, the initiation of the North American Monsoon (Adams and Comrie, 1997). 2.3. Trends in isentropic surfaces For each summer season and for each station, we computed the mean 315 K isentropic pressure level producing a 51-year time series from 1958 to 2008 (in recognition of 2008 being the extent of
Fig. 1. Mean pressure (kPa) of the 315 K isentropic surface for summer (JJA) 1958e2010. Black dots represent radiosonde locations used to compute the isentropic surface.
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Fig. 2. Standardized regression coefficients showing the strength of the linear trends in 315 K (JJA) isentropic levels from 1958 to 2008.
moisture influx has become more prevalent in the eastern half of the country with the higher correlation between isentropic pressure and time. The smaller correlations between the pressures of the isentropic surface and time in the western half of the country indicate smaller (but still positive) changes in moisture influx and adiabatic uplift over the fifty-one year period. Given the strong association between isentropic surface patterns and surface precipitation patterns (Wexler and Namias, 1938; Cerveny et al., 2011), it is possible that the trends identified in the summer isentropic 315 K surface should be reflected in corresponding trends in summer precipitation using a variety of possible daily and hourly indices. 3. Precipitation analysis
the hourly precipitation data available). We defined a criterion that a station needed at least 40 years of data to avoid elimination from further consideration. We then computed the strength of any linear trend in the data using simple linear regression with the year as the independent variable and the isentropic surface level as the dependent variable. In the simple regression case, the Pearson productemoment correlation coefficient, r, and the standardized regression coefficient, b, are the same and are unitless. Given a record of 51 years and relatively low levels of serial correlation within each time series, absolute values of r (or b) above 0.27 and 0.35 are statistically significant at the 95 per cent and 99 per cent levels of confidence. We used several different linear and nonlinear trend techniques (e.g., deterministic trend from BoxeJenkins modeling, ManneKendall rank statistic) and found no meaningful change in the results. The values of r (or b) averaged þ0.32 for the 46 stations and ranged from þ0.03 to þ0.55 (Fig. 2). Fig. 2 shows the largest values in the southern Plains (e.g., Texas and Oklahoma) and New England areas with relatively low values in the Southwest. The isolines were produced using universal kriging and the smooth pattern they depict explains 27.4 per cent of the variance in the original r values. The twenty seven per cent of explained variance reinforces the interpretation of only weak correlations between time and the pressure levels of the 315 K isentropic surface in the Southwest and Northwest. Higher correlations exist between the pressure levels of the 315 K isentropic surface values and time in the southern Plains states and the New England area. Interpretation of these findings follows past descriptive research dating back as early as in Wexler and Namias (1938). Specifically, higher pressures of an isentropic surface are associated with moisture influx. That adiabatic flow from higher pressures (lower heights) of the isentropic surface to lower pressure is associated with convective precipitation. The pattern revealed in Fig. 2 suggests that
3.1. Trends in daily precipitation characteristics We selected precipitation stations in the conterminous United States that are included in the popular and widely-used Global Historical Climatology Network (GHCN) e Daily database provided to us by scientists at the National Climate Data Center (NCDC) (Durre et al., 2008; Menne et al., 2010). The GHCN-D is the world’s largest collection of daily climatological data and is considered well-suited for monitoring and assessment activities related to the frequency and magnitude of extremes. The data have undergone considerable quality assurance, the data are updated frequently, and all data are downloadable from the NCDC website. There are 1218 stations in the conterminous United States included in the GHCN-D dataset. Given our study period of 1958e2008, we eliminated stations with more than 10 per cent missing daily data over that time interval, thereby leaving a network of 865 stations. For each summer season, we calculated five different indices of precipitation activity including the total precipitation, the frequency of days with precipitation, the intensity defined as the total divided by the frequency, and the number of days with 50 mm of rainfall. The fifth measure involved determining the frequency distribution for all daily events at a station over the 51-year study period. We then determined the value above which constituted the top 10 per cent of the total precipitation. For each summer season, we determined how many daily events exceeded that threshold; the value averaged over all stations was 126 mm and these values were clearly highest in the rainiest parts of the country in the summer months. Using the year of record as the independent variable and the rainfall totals as the dependent variable, we again calculated the linear trend using simple regression analysis. The resulting map (Fig. 3) shows that precipitation totals have generally increased in most areas of the country, particularly in the northeast quarter of the country from the Great Lakes through the New England states;
Fig. 3. Standardized regression coefficients showing strength of linear trend over the 1958e2008 time period for total precipitation.
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precipitation totals declined in the central portion of the Rockies. A universal kriging interpolated surface explained 35.2 per cent of the spatial variance in the trend values and showed highest positive values in the western Great Lakes area and in New England, and the largest negative values centered over northern Nevada, western Oregon, and southern Idaho. The four map pattern correlation coefficients between the trends in precipitation totals and the other four indices of precipitation characteristics ranged from þ0.53 to þ0.56, and even when accounting for spatial autocorrelation, the coefficients are significant at the 99 per cent confidence level. Basically, areas where precipitation totals increased (decreased) tended to be the areas where intensity and/or frequency increased (decreased) as well. For example, the trends for the events contributing to the top 10 per cent of precipitation totals, and immediately, one recognizes that the increase has occurred in the northeastern quarter while a decrease has been occurring in the central western United States. We conducted a principal components analysis on the spatial variance for the five precipitation indices and found that the first component explains 84.0 per cent of the variance in the data with loadings ranging from þ0.88 for intensity to þ0.98 for both frequency and precipitation total. These analyses show that despite their exact definition, the five indices basically captured temporal variance in overall precipitation totals at each station. 3.2. Trends in hourly precipitation characteristics Next, hourly precipitation data were collected from the United States Hourly Precipitation Dataset (DS 3240), available through the National Climatic Data Center (Hammer and Steurer, 2000). For this analysis, we identified 83 first-order weather stations operated by the National Weather Service as having a complete record during the study period (from 1958 to 2008), which included having hourly precipitation measured to 0.254 mm. Precipitation data from June, July, and August were placed in a matrix which included the average event duration and the average precipitation per event, following Brommer et al.’s (2007) definition of a precipitation event and duration calculation. Following the determination that the data were normally distributed, we analyzed the summer season event duration and average precipitation per event using linear regression to diagnose the statistical significance of any trends over the study period in a manner similar to that described in the previous section. Twelve of the 83 stations had statistically-significant trends, with all but two being positive. Longer-duration precipitation events were generally located in central United States, along the South Carolina and North Carolina coasts, and in the eastern Great Lakes region. Shorter-duration summer precipitation events were noted at two locations; in the northern Rocky Mountains (centered around Billings, Montana) and in the northeastern regions of New England (near Caribou, Maine). A smaller subset of eight stations was identified as having statistically-significant changes in average precipitation per event during summer. Five of the eight stations had significant increases in the average amount of precipitation per event, including Boise, Idaho; Moline, Illinois; Caribou, Maine; Buffalo, New York; and Amarillo, Texas. During the period of record, Albuquerque, New Mexico; Charleston, South Carolina; and Rapid City, South Dakota all experienced a decrease in the average amount of precipitation per event. 4. Precipitation e isentropic link Climatological isentropic analysis, although first implemented many decades ago, provides an interesting means of accounting for seasonal trends in precipitation. As researchers ranging from
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Namias (1940) to Cerveny et al. (2011) indicated, climatological isentropic analysis reasonably depicts moisture flows and adiabatic uplift patterns. This is particularly evident in the strongly convective character of the conterminous United States summer. Consequently, calculation of trends in the spatial pattern of the summer 315 K isentropic surface should reflect corresponding changes in the regional character of precipitation over the last fifty years. We identified positive correlations between time and the pressure levels of the 315 K isentropic surface in the southern Plains states and the New England area. Such correlations suggest long-term rising of pressures (lowering heights) for the isentropic surface (and therefore enhanced moisture inflow) into those regions. Much weaker (but still positive) correlations with time and the pressure levels of the 315 K isentropic surface are found in the Southwest and in the Northwest. Given that enhanced moisture flow is associated with lowering elevations of isentropic surfaces, we hypothesized corresponding changes in the precipitation. Recognizing that the map pattern correlation coefficients could be impacted by deviations from normality in the spatial data, we evaluated these variables for normality (a Gaussian distribution) using the standardized coefficients of skewness, z1, and kurtosis, z2, calculated as:
hP z1 ¼
N i ¼ 1 ðxi
XÞ3 =N
ih P
N i ¼ 1 ðxi
XÞ2 =N
i3=2 (2)
ð6=NÞ1=2
and
( hP
N i ¼ 1 ðxi
z2 ¼
4
XÞ =N
ih P
N i ¼ 1 ðxi
ð24=NÞ1=2
2
XÞ =N
i2
) 3 (3)
where the resulting z values are compared against a t-value deemed appropriate for a selected level of confidence. If the absolute value of z1 or z2 exceeds the selected value of t, a significant deviation from the normal curve is confirmed. Otherwise, no statistically-significant deviation from a normal distribution is determined (the null hypothesis that the samples came from a normal distribution cannot be rejected). We tested the isentropic values and all precipitation variables discussed below that were involved in the map pattern correlation analyses, and none showed a significant deviation from normality in terms of skewness or kurtosis. Using the Global Historical Climatology Network (GHCN) e Daily precipitation database and the United States Hourly Precipitation Dataset (DS 3240), we compared the map pattern correlations between the trends in isentropic surfaces and the trends in both precipitation daily totals and in hourly durations. First, we find that a strong correlation exists between the trends in the isentropic surface and the daily precipitation. A correlation of þ0.67 between the mapped patterns of the two trends (isentropic and daily precipitation) across the conterminous United States indicates that the precipitation increases are likely influenced by a stronger moisture influx, particularly in the southern Plains states and the New England area, as indicated by the lowering elevation of the 315 K isentropic surface over the last fifty years. A similar but weaker positive correlation (þ0.44) is evident between the trends in daily intensity of precipitation and the trends in the pressure levels of the 315 K isentropic surface. The differential lowering of the isentropic surface over time (Fig. 2) would change the gradient of the isentropic surface and, consequently, the adiabatic uplift (Namias, 1940). An enhanced gradient would aid in
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the more rapid uplift of air masses and, potentially, a greater intensity of rainfall over the course of a day. However, changes in large-scale circulation may only provide a portion of the explanation for changes in the precipitation pattern. Other, particularly local-scale factors, such as changes in cloud microphysics, and local heating/cooling by pollutants, may also contribute to these changes. Therefore, in a similar fashion to constant pressure surface anomaly analysis, the analysis of the isentropic surface may not significantly aid understanding when these non-large-scale factors are affecting the local precipitation pattern. More local detailed information may be necessary for complete understanding. However, the spatial relationship between the trends in the isentropic surface and the trends in the hourly precipitation duration is only 0.07. This suggests that the individual hourly character of precipitation across the summer conterminous United States is perhaps more influenced by the localized character of the specific convective storm and not by the long-term trends in the moisture flow and adiabatic uplift which are represented by trends in the isentropic surface. As the isentropic network (46 stations of 60 stations) and the precipitation network (83 first-order stations, 865 GHCN stations) do not match, we cannot directly correlate values between the two. An alternative approach to investigating the linkage between precipitation patterns and isentropic heights involves treating the conterminous United States as one areal unit (it covers only 1.54% of the Earth’s surface). For each precipitation variable (total, frequency, intensity, etc.), the time series of summer values at each station was converted into z-scores with a mean of zero and a standard deviation of one. The z-scores were then averaged across all stations with non-missing values for each summer season from 1958 to 2008. This procedure produced a time series matrix with 41 rows, one for each year from 1958 to 2008, and six columns representing the mean z-scores for precipitation total, frequency, intensity, duration, the number of events in the ninetieth percentile, and the number of daily events 50 mm. The matrix was subjected to a principal components analysis with varimax rotation, and the first (and dominant) component had high loadings (0.85 and 0.96, respectively) for precipitation total and precipitation frequency. A plot of the time series of the first eigenvector is given in Fig. 4 and visually demonstrates a slight upward trend in precipitation as revealed by the first eigenvector; however, the trend upward is not significant at the p ¼ 0.05 level of confidence. The component scores are plotted against the mean isentropic pressure level for the United States, and as seen in Fig. 5, a highly statistically-significant (p < 0.01) negative Pearson productemoment correlation coefficient of 0.46 exists between the two variables.
Fig. 5. Scatterplot of the first principal components eigenvector (loading highly on precipitation total and precipitation frequency) against mean isentropic pressure level for the United States exhibiting a highly statistically-significant (p < 0.01) negative Pearson productemoment correlation coefficient of 0.46 between the two variables.
This finding reinforces our general conclusion that higher values of precipitation are associated with higher isentropic pressures (lower isentropic heights). Components highly related to intensity or duration of precipitation were not significantly related to the nationally-averaged isentropic height time series. 5. Conclusions Climatological isentropic analysis as pioneered by Namias in the 1930s and 1940s provides an interesting means to assess the influence of moisture influx and adiabatic uplift on precipitation and related moisture parameters. We have identified a strong linkage between the long-term trends in the daily summer precipitation totals for the United States and the trends in the pressure levels of the 315 K isentropic surface over the last fifty years. Specifically, we have identified positive correlations between time and the pressure levels of the 315 K isentropic surface in the southern Plains states and the New England area. Such correlations suggest long-term rising of pressures (lowering heights) for the isentropic surface (and therefore enhanced moisture inflow) into those regions. Conversely, weaker correlations with time and the isentropic surface are found in the Southwest and in the Northwest. Incorporating these results with data from two well-accepted precipitation databases, we then compared the map pattern correlations between the trends in isentropic surfaces and the trends in both precipitation daily totals and in hourly durations. The strongest correlations (þ0.67) exist between the trends in the isentropic surface and those for daily precipitation totals. This suggests that the precipitation increases are likely influenced by a stronger moisture influx associated with the growing isentropic slope. A weaker but still significant positive correlation (þ0.44) is evident between the trends in daily precipitation intensity and the trends in the 315 K isentropic surface. However, the spatial relationship between the trends in the isentropic surface and the trends in the hourly precipitation duration is only 0.07 indicating no significant accounting of trends in duration by corresponding isentrope surface trends. Continued study of aspects of the relatively neglected analysis of climatological isentropes will likely add to our understanding of the physical changes in precipitation patterns across the United States and the world. Acknowledgment
Fig. 4. Time series plot of the first principal component eigenvector score (loading highly on precipitation total and precipitation frequency) against time.
This research was funded in part by a grant from the National Science Foundation (0751790). The authors would like to thank the
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two anonymous reviewers for evaluating the manuscript and for their valuable comments. References Adams, A.K., Comrie, A.C., 1997. The North American monsoon. Bulletin of the American Meteorological Society 10, 2197e2213. Brommer, D.M., Cerveny, R.S., Balling Jr., R.C., 2007. Characteristics of long-duration precipitation events across the United States. Geophysical Research Letters 22 (L22712). Cerveny, R.S., DeBiasse, K., Pace, M., Balling Jr., R.C., Ellis, A.W., 2011. Re-analysis and extension of Namias’s climatological isentropic analysis: detection and evaluation of monsoonal, severe storm, drought, and flood events. Annals of the Association of American Geographers 101, 1e17. De Conning, E., 2000. PCGRIDDS-based isentropic analysis as a forecasting tool in the South African Weather Bureau. Water SA 3, 377e387. Durre, I., Menne, M.J., Vose, R.S., 2008. Strategies for evaluating quality assurance procedures. Journal of Applied Meteorology and Climatology 47, 1785e1791. Forecast Systems Laboratory, 1997. Radiosonde Data of North America, 1946e1996 [CD-Rom]. National Climatic Data Center, Asheville.
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Hammer, G., Steurer, P., 2000. Data Documentation for Data Set 3240 (DSI 3240) Hourly Precipitation Data. Tech. Doc. TD-3240. National Climatic Data Center, Asheville, NC, 19 pp. Holton, J.R., 1992. An Introduction to Dynamic Meteorology, third ed. Academic Press London, 511 pp. Hoskins, B.J., 1991. Towards a PVq view of the general circulation. Tellus 43, 27e35. Kalnay, E., Kanamitsu, M., Kistler, R., Collins, W., Deaven, D., Gandin, L., Iredell, M., Saha, S., White, G., Woollen, J., Zhu, Y., Leetmaa, A., Reynolds, B., Chelliah, M., Ebisuzaki, W., Higgins, W., Janowiak, J., Mo, K.C., Ropelewski, C., Wang, J., Jenne, R., Joseph, D., 1996. The NCEP/NCAR 40year reanalysis project. Bulletin of the American Meteorological Society 77, 437e471. Menne, M.J., Williams, C.N., Palecki, M.A., 2010. On the reliability of the US surface temperature record. Journal of Geophysical Research e Atmospheres 115 (D11108). doi:10.1029/2009JD013094. Namias, J., 1940. Air Mass and Isentropic Analysis, fifth ed. American Meteorology Society, Milton, 232 pp. Wexler, H., Namias, J., 1938. Mean monthly isentropic charts and their relation to departures of summer rainfall. EOS, Transactions, American Geophysical Union 19th Annual Meeting, pp. 164e170.
Contents lists available at ScienceDirect
Atmospheric Environment journal homepage: www.elsevier.com/locate/atmosenv
Long-term precipitation trend as a function of isentropic variability Robert C. Balling Jr. a, Kimberly DeBiasse a, Matthew B. Pace a, Randall S. Cerveny a, *, David M. Brommer b a b
School of Geographical Sciences & Urban Planning, Arizona State University, Tempe, AZ 85302-0104, USA Department of Geography, University of Alabama, Tuscaloosa, AL 35487-0322, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 December 2010 Received in revised form 15 June 2011 Accepted 5 July 2011
Analysis of trends in climatological isentropes provides a means of evaluating seasonal precipitation trends. Past research has indicated that isentropic patterns are linked to moisture influx and adiabatic uplift. We calculate trends across the summer 315 K isentropic surface for the conterminous United States over the last fifty years. We identify positive correlations between time and the pressure levels of the 315 K isentropic surface in the southern Plains states and the New England area. Such correlations suggest long-term rising of pressures (lowering heights) for the isentropic surface (and therefore enhanced moisture inflow) into those regions. Weaker correlations with time and the isentropic surface are found in the Southwest and in the Northwest. Using two well-accepted precipitation databases, we compare the map pattern correlations between the trends in isentropic surfaces and the trends in both precipitation daily totals and in hourly durations. A strong correlation (þ0.67) exists between the trends in the isentropic surface and the daily precipitation and indicates that the precipitation increases are likely influenced by a stronger moisture influx. A weaker positive correlation (þ0.44) is evident between the trends in daily precipitation intensity and the trends in the 315 K isentropic surface. However, the spatial relationship between the trends in the isentropic surface and the trends in the hourly precipitation duration is only 0.07 indicating no significant accounting of trends in duration by corresponding isentrope surface trends. Continued study of the relatively neglected analysis of climatological isentropes will add to our understanding of the physical changes in precipitation patterns across the United States. Published by Elsevier Ltd.
Keywords: Isentropic surface Precipitation characteristics Climate change
1. Introduction One key to achieving a complete understanding of climate change is to produce a clear visualization of climate variables (e.g., precipitation) and the climatological processes that influence those variables. However, many atmospheric visualizations, such as upper-air isobaric analyses, are based on utilitarian needs of short-term meteorological operations (e.g., aviation) and were not created to necessarily demonstrate or analyze climatic processes. Isentropic analysis is based on the concept of dry adiabatic warming and cooling of atmospheric parcels through uplift or descent. In isentropic analysis, the analyst computes the pressure level associated with a given potential temperature (q) value, which is the temperature of an air parcel undergoing compression or expansion adiabatically to a pressure of 100 kPa (1000 mb). Given such a definition, a set of potential temperatures can be produced
* Corresponding author. E-mail address: [email protected] (R.S. Cerveny). 1352-2310/$ e see front matter Published by Elsevier Ltd. doi:10.1016/j.atmosenv.2011.07.013
for each rawinsonde sounding, throughout its upward movement. Normally, a specific isentropic temperature (e.g., q ¼ 305 K) is selected and the pressure (or, in early research, the height) corresponding to that isentropic value is plotted across the network of rawinsonde stations. Previous researchers have highlighted the usefulness of climatological isentropic analyses in identifying seasonal moisture and precipitation patterns (Namias, 1940; Cerveny et al., 2011) and longterm drought patterns (Wexler and Namias, 1938; Cerveny et al., 2011). In this study, we focus on how trends and variations in isentropic surfaces are related to trends and variations in characteristics of precipitation. As climatological isentropic research’s originator Jerome Namias and others have stressed, the primary advantage of isentropic analysis is that it “offers the ability to look at atmospheric motion in the way it actually happens e i.e., in three dimensions due to the fact that isentropic surfaces follow the true motion of a parcel” (De Conning, 2000, p. 377). Namias himself noted that the primary functions of the isentropic chart were (1) to facilitate the study of the identification and thermodynamic modification of large-scale air currents, and (2) to present a clear-cut picture of the major patterns of flow of atmospheric currents (Namias, 1940).
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2. Isentropic analysis 2.1. Theory of isentropic analysis The climatological aspects of isentropic analysis, the use and interpretation of atmospheric charts representing surfaces of constant potential temperature, were first introduced as a research tool by Namias in the 1930s. Early researchers maintained that the primary advantage of this analysis was that “. isentropic surfaces . give a much better picture of flow pattern than fixed-level charts and show the dry and moist tongues. This form of analysis allows a much better correlation of rainfall-patterns with upper-air phenomena than was possible [with constant pressure charts] .” (Wexler and Namias, 1938, p. 164). If isentropic patterns are being modified by long-term forcing mechanisms, such as anthropogenic influences and/or solar variability, this would suggest that the moisture and adiabatic uplift regions, and hence precipitation patterns, are also being impacted by that variability. Identification of any changes in uplift regions would be useful to forecasters and water managers. Consequently, we examine the spatial correlation of the trends in seasonal precipitation with changes in the isentropic surface. Potential temperature (q) as derived from one of the three Poisson’s relationships (Holton, 1992), can be expressed as:
R p cp q ¼ T s p
(1)
where T is the ambient temperature (K), ps is a standard reference pressure (100 kPa or 1000 hPa), p is the pressure, R is the gas constant for dry air (287 J K1 kg1), and cp is the specific heat of dry air at constant pressure (1004 J K1 kg1). Potential temperature is the corresponding temperature of a parcel of air moved adiabatically from its original pressure to 100 kPa. Therefore, movement along a constant potential temperature path is an adiabatic process. Although the majority of isentropic analysis since Namias’ work in the 1930s and 1940s has focused on the concepts surrounding isentropic potential vorticity (Hoskins, 1991), we are applying Namias’ original style of climatological isentropic analysis such as the one used in drought depiction and prediction (e.g., Wexler and Namias, 1938; Cerveny et al., 2011). 2.2. Mean isentropic surface Our modern isentropic analyses incorporate data from 1958 to 2010 generated using the raw sounding data from the CD-ROM “Radiosonde Data of North America 1946e1996” with updates to 2010, which is issued by the Forecast Systems Laboratory and National Climatic Data Center (Forecast Systems Laboratory, 1997). Although, traditionally the National Centers for Environmental Prediction
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(NCEP) reanalysis data (Kalnay et al., 1996) have been used for modern climate pattern analyses, those data are constructed on sigma pressure fields and consequently are not suitable for isentropic analysis. We extracted data from sixty long-term (1958e2008) upper-air rawinsonde sites, those stations which had a complete long-term record omitting those with large gaps of missing data. We then applied those data to equation (1) and the resultant potential temperature (isentrope) values to the nearest hectopascal (millibar) were interpolated for the average of the 00 UTC and 12 UTC soundings for the stations across the United States. Wind speed and direction were also interpolated at the various pressure and/or height levels associated with the isentropic surface. For this study, concentrating on the summer season, we selected the 315 K isentropic surface as suggested by Namias (1940) to ensure that the potential temperature surfaces would be above ground level. We calculated the average isentropic pressure for the summer months of June, July, and August (JJA) from all available 00 UTC and 12 UTC rawinsonde measurements over the 1958e2008 study period. Unfortunately, calculation of temporal trends in the isentropic dataset is complicated by the large number of missing months at many of the rawinsonde stations (due to station relocation and, unfortunately, some elimination of stations). We ultimately computed the linear trend in the data for the period 1958e2008 with the criterion that a station must have 40 years of valid continuous data for a given month; the trends were calculated separately for each month and averaged for the summer season. Fig. 1 shows the average pressure level of the summer (JJA) 315 K isentropic surface based on 46 stations of the original 60 stations that met our criteria based on missing data. The surface was produced using universal kriging and the resultant smooth surface explains 94.2 per cent of the spatial variance in the original data. The map depicts the classic monsoonal flow with higher pressure levels (lower heights) for the 315 K surface in the American Southwest. This isentropic trough arcs into the American Great Plains. Such an isentropic pattern, although identified using fewer stations with less temporal coverage, was described as far back in Namias (1940). As Namias (1940) noted, the occurrence of lower elevation/higher pressures of a given isentropic surface corresponds to adiabatic flow of moisture. The existence of this pronounced Southwest moisture tongue has been linked to the influx of moisture from the Gulf of California and Gulf of Mexico and, thereby, the initiation of the North American Monsoon (Adams and Comrie, 1997). 2.3. Trends in isentropic surfaces For each summer season and for each station, we computed the mean 315 K isentropic pressure level producing a 51-year time series from 1958 to 2008 (in recognition of 2008 being the extent of
Fig. 1. Mean pressure (kPa) of the 315 K isentropic surface for summer (JJA) 1958e2010. Black dots represent radiosonde locations used to compute the isentropic surface.
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Fig. 2. Standardized regression coefficients showing the strength of the linear trends in 315 K (JJA) isentropic levels from 1958 to 2008.
moisture influx has become more prevalent in the eastern half of the country with the higher correlation between isentropic pressure and time. The smaller correlations between the pressures of the isentropic surface and time in the western half of the country indicate smaller (but still positive) changes in moisture influx and adiabatic uplift over the fifty-one year period. Given the strong association between isentropic surface patterns and surface precipitation patterns (Wexler and Namias, 1938; Cerveny et al., 2011), it is possible that the trends identified in the summer isentropic 315 K surface should be reflected in corresponding trends in summer precipitation using a variety of possible daily and hourly indices. 3. Precipitation analysis
the hourly precipitation data available). We defined a criterion that a station needed at least 40 years of data to avoid elimination from further consideration. We then computed the strength of any linear trend in the data using simple linear regression with the year as the independent variable and the isentropic surface level as the dependent variable. In the simple regression case, the Pearson productemoment correlation coefficient, r, and the standardized regression coefficient, b, are the same and are unitless. Given a record of 51 years and relatively low levels of serial correlation within each time series, absolute values of r (or b) above 0.27 and 0.35 are statistically significant at the 95 per cent and 99 per cent levels of confidence. We used several different linear and nonlinear trend techniques (e.g., deterministic trend from BoxeJenkins modeling, ManneKendall rank statistic) and found no meaningful change in the results. The values of r (or b) averaged þ0.32 for the 46 stations and ranged from þ0.03 to þ0.55 (Fig. 2). Fig. 2 shows the largest values in the southern Plains (e.g., Texas and Oklahoma) and New England areas with relatively low values in the Southwest. The isolines were produced using universal kriging and the smooth pattern they depict explains 27.4 per cent of the variance in the original r values. The twenty seven per cent of explained variance reinforces the interpretation of only weak correlations between time and the pressure levels of the 315 K isentropic surface in the Southwest and Northwest. Higher correlations exist between the pressure levels of the 315 K isentropic surface values and time in the southern Plains states and the New England area. Interpretation of these findings follows past descriptive research dating back as early as in Wexler and Namias (1938). Specifically, higher pressures of an isentropic surface are associated with moisture influx. That adiabatic flow from higher pressures (lower heights) of the isentropic surface to lower pressure is associated with convective precipitation. The pattern revealed in Fig. 2 suggests that
3.1. Trends in daily precipitation characteristics We selected precipitation stations in the conterminous United States that are included in the popular and widely-used Global Historical Climatology Network (GHCN) e Daily database provided to us by scientists at the National Climate Data Center (NCDC) (Durre et al., 2008; Menne et al., 2010). The GHCN-D is the world’s largest collection of daily climatological data and is considered well-suited for monitoring and assessment activities related to the frequency and magnitude of extremes. The data have undergone considerable quality assurance, the data are updated frequently, and all data are downloadable from the NCDC website. There are 1218 stations in the conterminous United States included in the GHCN-D dataset. Given our study period of 1958e2008, we eliminated stations with more than 10 per cent missing daily data over that time interval, thereby leaving a network of 865 stations. For each summer season, we calculated five different indices of precipitation activity including the total precipitation, the frequency of days with precipitation, the intensity defined as the total divided by the frequency, and the number of days with 50 mm of rainfall. The fifth measure involved determining the frequency distribution for all daily events at a station over the 51-year study period. We then determined the value above which constituted the top 10 per cent of the total precipitation. For each summer season, we determined how many daily events exceeded that threshold; the value averaged over all stations was 126 mm and these values were clearly highest in the rainiest parts of the country in the summer months. Using the year of record as the independent variable and the rainfall totals as the dependent variable, we again calculated the linear trend using simple regression analysis. The resulting map (Fig. 3) shows that precipitation totals have generally increased in most areas of the country, particularly in the northeast quarter of the country from the Great Lakes through the New England states;
Fig. 3. Standardized regression coefficients showing strength of linear trend over the 1958e2008 time period for total precipitation.
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precipitation totals declined in the central portion of the Rockies. A universal kriging interpolated surface explained 35.2 per cent of the spatial variance in the trend values and showed highest positive values in the western Great Lakes area and in New England, and the largest negative values centered over northern Nevada, western Oregon, and southern Idaho. The four map pattern correlation coefficients between the trends in precipitation totals and the other four indices of precipitation characteristics ranged from þ0.53 to þ0.56, and even when accounting for spatial autocorrelation, the coefficients are significant at the 99 per cent confidence level. Basically, areas where precipitation totals increased (decreased) tended to be the areas where intensity and/or frequency increased (decreased) as well. For example, the trends for the events contributing to the top 10 per cent of precipitation totals, and immediately, one recognizes that the increase has occurred in the northeastern quarter while a decrease has been occurring in the central western United States. We conducted a principal components analysis on the spatial variance for the five precipitation indices and found that the first component explains 84.0 per cent of the variance in the data with loadings ranging from þ0.88 for intensity to þ0.98 for both frequency and precipitation total. These analyses show that despite their exact definition, the five indices basically captured temporal variance in overall precipitation totals at each station. 3.2. Trends in hourly precipitation characteristics Next, hourly precipitation data were collected from the United States Hourly Precipitation Dataset (DS 3240), available through the National Climatic Data Center (Hammer and Steurer, 2000). For this analysis, we identified 83 first-order weather stations operated by the National Weather Service as having a complete record during the study period (from 1958 to 2008), which included having hourly precipitation measured to 0.254 mm. Precipitation data from June, July, and August were placed in a matrix which included the average event duration and the average precipitation per event, following Brommer et al.’s (2007) definition of a precipitation event and duration calculation. Following the determination that the data were normally distributed, we analyzed the summer season event duration and average precipitation per event using linear regression to diagnose the statistical significance of any trends over the study period in a manner similar to that described in the previous section. Twelve of the 83 stations had statistically-significant trends, with all but two being positive. Longer-duration precipitation events were generally located in central United States, along the South Carolina and North Carolina coasts, and in the eastern Great Lakes region. Shorter-duration summer precipitation events were noted at two locations; in the northern Rocky Mountains (centered around Billings, Montana) and in the northeastern regions of New England (near Caribou, Maine). A smaller subset of eight stations was identified as having statistically-significant changes in average precipitation per event during summer. Five of the eight stations had significant increases in the average amount of precipitation per event, including Boise, Idaho; Moline, Illinois; Caribou, Maine; Buffalo, New York; and Amarillo, Texas. During the period of record, Albuquerque, New Mexico; Charleston, South Carolina; and Rapid City, South Dakota all experienced a decrease in the average amount of precipitation per event. 4. Precipitation e isentropic link Climatological isentropic analysis, although first implemented many decades ago, provides an interesting means of accounting for seasonal trends in precipitation. As researchers ranging from
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Namias (1940) to Cerveny et al. (2011) indicated, climatological isentropic analysis reasonably depicts moisture flows and adiabatic uplift patterns. This is particularly evident in the strongly convective character of the conterminous United States summer. Consequently, calculation of trends in the spatial pattern of the summer 315 K isentropic surface should reflect corresponding changes in the regional character of precipitation over the last fifty years. We identified positive correlations between time and the pressure levels of the 315 K isentropic surface in the southern Plains states and the New England area. Such correlations suggest long-term rising of pressures (lowering heights) for the isentropic surface (and therefore enhanced moisture inflow) into those regions. Much weaker (but still positive) correlations with time and the pressure levels of the 315 K isentropic surface are found in the Southwest and in the Northwest. Given that enhanced moisture flow is associated with lowering elevations of isentropic surfaces, we hypothesized corresponding changes in the precipitation. Recognizing that the map pattern correlation coefficients could be impacted by deviations from normality in the spatial data, we evaluated these variables for normality (a Gaussian distribution) using the standardized coefficients of skewness, z1, and kurtosis, z2, calculated as:
hP z1 ¼
N i ¼ 1 ðxi
XÞ3 =N
ih P
N i ¼ 1 ðxi
XÞ2 =N
i3=2 (2)
ð6=NÞ1=2
and
( hP
N i ¼ 1 ðxi
z2 ¼
4
XÞ =N
ih P
N i ¼ 1 ðxi
ð24=NÞ1=2
2
XÞ =N
i2
) 3 (3)
where the resulting z values are compared against a t-value deemed appropriate for a selected level of confidence. If the absolute value of z1 or z2 exceeds the selected value of t, a significant deviation from the normal curve is confirmed. Otherwise, no statistically-significant deviation from a normal distribution is determined (the null hypothesis that the samples came from a normal distribution cannot be rejected). We tested the isentropic values and all precipitation variables discussed below that were involved in the map pattern correlation analyses, and none showed a significant deviation from normality in terms of skewness or kurtosis. Using the Global Historical Climatology Network (GHCN) e Daily precipitation database and the United States Hourly Precipitation Dataset (DS 3240), we compared the map pattern correlations between the trends in isentropic surfaces and the trends in both precipitation daily totals and in hourly durations. First, we find that a strong correlation exists between the trends in the isentropic surface and the daily precipitation. A correlation of þ0.67 between the mapped patterns of the two trends (isentropic and daily precipitation) across the conterminous United States indicates that the precipitation increases are likely influenced by a stronger moisture influx, particularly in the southern Plains states and the New England area, as indicated by the lowering elevation of the 315 K isentropic surface over the last fifty years. A similar but weaker positive correlation (þ0.44) is evident between the trends in daily intensity of precipitation and the trends in the pressure levels of the 315 K isentropic surface. The differential lowering of the isentropic surface over time (Fig. 2) would change the gradient of the isentropic surface and, consequently, the adiabatic uplift (Namias, 1940). An enhanced gradient would aid in
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the more rapid uplift of air masses and, potentially, a greater intensity of rainfall over the course of a day. However, changes in large-scale circulation may only provide a portion of the explanation for changes in the precipitation pattern. Other, particularly local-scale factors, such as changes in cloud microphysics, and local heating/cooling by pollutants, may also contribute to these changes. Therefore, in a similar fashion to constant pressure surface anomaly analysis, the analysis of the isentropic surface may not significantly aid understanding when these non-large-scale factors are affecting the local precipitation pattern. More local detailed information may be necessary for complete understanding. However, the spatial relationship between the trends in the isentropic surface and the trends in the hourly precipitation duration is only 0.07. This suggests that the individual hourly character of precipitation across the summer conterminous United States is perhaps more influenced by the localized character of the specific convective storm and not by the long-term trends in the moisture flow and adiabatic uplift which are represented by trends in the isentropic surface. As the isentropic network (46 stations of 60 stations) and the precipitation network (83 first-order stations, 865 GHCN stations) do not match, we cannot directly correlate values between the two. An alternative approach to investigating the linkage between precipitation patterns and isentropic heights involves treating the conterminous United States as one areal unit (it covers only 1.54% of the Earth’s surface). For each precipitation variable (total, frequency, intensity, etc.), the time series of summer values at each station was converted into z-scores with a mean of zero and a standard deviation of one. The z-scores were then averaged across all stations with non-missing values for each summer season from 1958 to 2008. This procedure produced a time series matrix with 41 rows, one for each year from 1958 to 2008, and six columns representing the mean z-scores for precipitation total, frequency, intensity, duration, the number of events in the ninetieth percentile, and the number of daily events 50 mm. The matrix was subjected to a principal components analysis with varimax rotation, and the first (and dominant) component had high loadings (0.85 and 0.96, respectively) for precipitation total and precipitation frequency. A plot of the time series of the first eigenvector is given in Fig. 4 and visually demonstrates a slight upward trend in precipitation as revealed by the first eigenvector; however, the trend upward is not significant at the p ¼ 0.05 level of confidence. The component scores are plotted against the mean isentropic pressure level for the United States, and as seen in Fig. 5, a highly statistically-significant (p < 0.01) negative Pearson productemoment correlation coefficient of 0.46 exists between the two variables.
Fig. 5. Scatterplot of the first principal components eigenvector (loading highly on precipitation total and precipitation frequency) against mean isentropic pressure level for the United States exhibiting a highly statistically-significant (p < 0.01) negative Pearson productemoment correlation coefficient of 0.46 between the two variables.
This finding reinforces our general conclusion that higher values of precipitation are associated with higher isentropic pressures (lower isentropic heights). Components highly related to intensity or duration of precipitation were not significantly related to the nationally-averaged isentropic height time series. 5. Conclusions Climatological isentropic analysis as pioneered by Namias in the 1930s and 1940s provides an interesting means to assess the influence of moisture influx and adiabatic uplift on precipitation and related moisture parameters. We have identified a strong linkage between the long-term trends in the daily summer precipitation totals for the United States and the trends in the pressure levels of the 315 K isentropic surface over the last fifty years. Specifically, we have identified positive correlations between time and the pressure levels of the 315 K isentropic surface in the southern Plains states and the New England area. Such correlations suggest long-term rising of pressures (lowering heights) for the isentropic surface (and therefore enhanced moisture inflow) into those regions. Conversely, weaker correlations with time and the isentropic surface are found in the Southwest and in the Northwest. Incorporating these results with data from two well-accepted precipitation databases, we then compared the map pattern correlations between the trends in isentropic surfaces and the trends in both precipitation daily totals and in hourly durations. The strongest correlations (þ0.67) exist between the trends in the isentropic surface and those for daily precipitation totals. This suggests that the precipitation increases are likely influenced by a stronger moisture influx associated with the growing isentropic slope. A weaker but still significant positive correlation (þ0.44) is evident between the trends in daily precipitation intensity and the trends in the 315 K isentropic surface. However, the spatial relationship between the trends in the isentropic surface and the trends in the hourly precipitation duration is only 0.07 indicating no significant accounting of trends in duration by corresponding isentrope surface trends. Continued study of aspects of the relatively neglected analysis of climatological isentropes will likely add to our understanding of the physical changes in precipitation patterns across the United States and the world. Acknowledgment
Fig. 4. Time series plot of the first principal component eigenvector score (loading highly on precipitation total and precipitation frequency) against time.
This research was funded in part by a grant from the National Science Foundation (0751790). The authors would like to thank the
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two anonymous reviewers for evaluating the manuscript and for their valuable comments. References Adams, A.K., Comrie, A.C., 1997. The North American monsoon. Bulletin of the American Meteorological Society 10, 2197e2213. Brommer, D.M., Cerveny, R.S., Balling Jr., R.C., 2007. Characteristics of long-duration precipitation events across the United States. Geophysical Research Letters 22 (L22712). Cerveny, R.S., DeBiasse, K., Pace, M., Balling Jr., R.C., Ellis, A.W., 2011. Re-analysis and extension of Namias’s climatological isentropic analysis: detection and evaluation of monsoonal, severe storm, drought, and flood events. Annals of the Association of American Geographers 101, 1e17. De Conning, E., 2000. PCGRIDDS-based isentropic analysis as a forecasting tool in the South African Weather Bureau. Water SA 3, 377e387. Durre, I., Menne, M.J., Vose, R.S., 2008. Strategies for evaluating quality assurance procedures. Journal of Applied Meteorology and Climatology 47, 1785e1791. Forecast Systems Laboratory, 1997. Radiosonde Data of North America, 1946e1996 [CD-Rom]. National Climatic Data Center, Asheville.
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