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Effects of Temperature Anomalies on the Palmer
Drought Severity Index in the Central United States

An Observational Analysis


In this section, we use climate data and calculated Z-index and PDSI to further illustrate the above theoretical results and separate the effects of precipitation and temperature on the PDSI.

Data and method

The climate data used in this analysis cover the southeast portion of Missouri (Region 1) and the central Great Plains of the United States (Region 2) (Figure 1). The former has a humid temperate climate and the latter has a dry temperate climate. Historical monthly precipitation and temperature data for the two regions were obtained from the US National Climatic Data Center (NCDC). The data were quality checked and are continuous.

A calculation method of Z-index and PDSI developed at the NCDC was used. Soil parameters for each of the regions were obtained from US Department of Agriculture (USDA) Soil Testing Laboratory at Lincoln, NE.

GIF -- Location of Study Areas Map; Region 1 covers SE quarter of Missouri, Region 2 covers Nebraska, Kansas, and eastern Wyoming and Colorado
Figure 1.  The geographical location of the study areas. Region 1 covers the eastern Ozark Plateau in Missouri and Region 2 covers the Central Great Plains of the US (modified from the Central Great Plains Assessment, 1999)

Results

Using the historical data, we calculated Z-index and identified all the months which had Z values close to neutral (Z = 0). We further examined monthly temperature and precipitation for those months and selected the months that had near normal monthly temperature and precipitation. This neutral climate condition serves as the basis for comparison and identification of responses of Z to temperature and precipitation anomalies. We then recalculated Z-index, after adding a perturbation to the monthly temperature and precipitation, respectively, and examined the response of Z to the perturbation. According to Equation (5), the response of Z is the response of PDSI to temperature and precipitation anomalies.

Guttman (1991) reported a similar analysis but with a different approach in which he specified a month, e.g. November (see figures 1 and 2 in Guttman, 1991), and defined a neutral condition based on PHDI. He calculated PHDI from perturbed temperature and precipitation in a perpetual November time series, and determined PHDI sensitivity. In this study, we used composite monthly conditions from real data and examined Z and PDSI responses to temperature and precipitation anomalies. Another aspect of the study by Guttman (1991), relevant to the results described below, is that Guttman used 'temperature perturbations of plus and minus 1, 3, 5, and 10 degrees of Fahrenheit', and 'precipitation perturbations of 25 to 200 percent of the long-term, monthly averaged value' in his analysis. For the sites used in his study, such temperature perturbations were within 10-25% of the mean monthly temperatures. They were smaller, percentage-wise, than the smallest precipitation perturbations used in his study. In our study, we examine responses of Z to temperature and precipitation anomalies of the same magnitude relative to their mean monthly values, and discuss the difference between the magnitude of anomalies of temperature and precipitation as a separate issue.

Figure 2 shows average change in Z over the month of June from our procedure for Region 2. The results indicate that monthly Z-index changed from near neutral (-0.12) to -1.10 in response to a temperature increase of 1-2.5C, equivalent to 5-10% of monthly mean temperature for June in the region. It changed from -0.12 to -0.46, corresponding to precipitation decreases of similar magnitudes, i.e. same percentage of monthly mean precipitation. When we decreased temperature or increased precipitation by the proportional amounts, Z-index changed from near neutral to positive values of 0.80 and 0.24, respectively. Similar responses of Z to temperature and precipitation changes also were observed for Region 1. These changes contributed to monthly PDSI variations in those regions.

GIF -- Temperature effect line (solid) and Rainfall effect line (dashed) plotted on graph of Z-index vs. DT/DP
Figure 2.  Response of Z-index to temperature and precipitation perturbations for June in Region 2

These results confirm that for changes of similar magnitude of temperature and precipitation the Z-index and PDSI were about equally affected, with a slightly bigger effect from temperature anomalies. They are consistent with the theoretical results of the previous section and suggest that the PDSI cannot directly measure the fluctuations of precipitation when temperature anomalies coexist. They are also consistent with results of calculations by other methods. For example, Abramopoulos et al. (1988) show in their general circulation modelling study that evaporation and transpiration can consume up to 80% of rainfall. In addition, they found that the efficiency of drying due to temperature anomalies is as high as that due to rainfall shortages.

Because the temperature fluctuation is smaller than the precipitation fluctuation, we observe larger responses of Z and PDSI to precipitation anomalies. Our examination of monthly temperature and precipitation data in Region 1 (1897-1995) and Region 2 (1948-1995) showed that 1 standard deviation (S.D.) of monthly temperature variation is about 10% of monthly average temperature for warm season months. On the other hand, 1 S.D. of monthly precipitation variation is about 50% of monthly mean precipitation in those months. Depending on a region's climate, large precipitation fluctuations can have considerable impact on PDSI. However, temperature anomalies are often dominant in PDSI variations from time to time. The PDSI variations actually result from a combination of both temperature and precipitation anomalies.

To further illustrate the latter point, we present in Figures 3 and 4 the correlation of PDSI and anomalies of precipitation and temperature for Regions 1 and 2, respectively. The PDSI was calculated from monthly precipitation and temperature for the period 1897-1995 for Region 1 and 1948-1995 for Region 2. Because there were often both precipitation and temperature anomalies in a month and both could be large for some months, we selected the months that had either temperature anomalies larger than the precipitation anomalies or precipitation anomalies larger than temperature anomalies, and divided them into two groups. Specifically, Group 1 has all the months that have absolute precipitation anomalies greater than or equal to 1 S.D. of the monthly means but have absolute temperature anomalies smaller than 1 S.D. of the monthly means for the same months. Group 2 has the same criterion but with precipitation anomalies smaller than the temperature anomalies. Group 1 has 216 elements (months) and Group 2 has 219 elements among 1176 monthly data for Region 1. There are 90 and 92 elements in Group 1 and Group 2, respectively, among 564 monthly data for Region 2. In these two groups, either the precipitation anomaly or the temperature anomaly was the major effect on PDSI. Thus, we can separately examine the effect of temperature and precipitation on PDSI.

GIF -- Scattered plot graphs for Region 1
Figure 3.  Correlations of PDSI versus regional average precipitation (a), temperature (b) and correlation of regional average precipitation versus temperature (c) for Region 1 (see text for details)

Figure 3(a) shows the relation of PDSI and monthly precipitation anomaly for Region 1. The black dots show the data from Group 1 with large monthly precipitation anomalies, and grey dots show all the 1176 data in the 98-year period. There is a positive correlation of 0.79 between the PDSI and monthly precipitation anomaly. Figure 3(b) shows a similar plot but for monthly temperature and PDSI, which reveals a negative correlation. The correlation coefficient is -0.35. Although this is smaller than the correlation coefficient between the PDSI and precipitation anomaly, it is above the 95% confidence level, 0.32, for the dataset (Steel and Torrie, 1960). It indicates that the temperature effect on the PDSI is statistically significant when the precipitation anomaly is not large. It is also worth pointing out that the number of elements in the two groups are nearly equal, suggesting an equal chance for either the precipitation or temperature anomaly to affect the PDSI for the region.

Figure 3(c) shows that there is no relationship between precipitation and temperature anomalies in Region 1. This result further indicates that the dependence of PDSI on temperature shown in Figure 3(b) is uniquely explained by temperature anomalies.

Figure 4 shows similar calculations for Region 2. Again, the correlation between the PDSI and temperature anomalies is statistically significant although its coefficient (-0.40) is smaller than the correlation coefficient between the PDSI and precipitation anomalies (0.69) for this region. However, because there is a negative correlation between the temperature and precipitation anomalies in this region, as shown in Figure 4(c), the negative correlation between the temperature anomaly and PDSI shown in Figure 4(b) might not be explicitly attributable to the temperature anomalies (Figure 4(a)).

GIF -- Scattered plot graphs for Region 2
Figure 4.  Correlations of PDSI versus regional average precipitation (a), temperature (b) and correlation of regional average precipitation versus temperature (c) for Region 2 (see text for details)

To resolve this ambiguity in the Region 2 results, we examined the monthly data of individual stations in Nebraska, which is in Region 2. We identified cases at different stations that had near normal rainfall but anomalous temperatures. A typical case is shown in Figure 5 for 1977-1979 at Auburn, NE.

GIF -- Three line graphs: Variations of monthly precipitation anomaly, temperature anomaly and PDSI for 1977-1979
Figure 5.  Variations of monthly precipitation anomaly (a), temperature anomaly (b) and corresponding PDSI (c) for 1977-1979 at Auburn, NE. The dashed-line in (c) shows calculated PDSI using monthly mean temperatures for the time period, and the dotted-line the PDSI using monthly mean temperatures plus a 2C increase of June, July and August temperatures

The solid curves in Figure 5(a) and (b) show recorded temperature and precipitation anomalies for the period. It was a very wet period from August to October 1977. The August rainfall amount was 206 mm above the average of 1897-1995 and was close to 3 S.D. of the station normal precipitation for that month. The soil remained wet through February of 1978. From June 1978 to December 1979, precipitation fluctuated around normal and the overall average was slightly above normal. There were two major cold periods in the winters of 1977-1978 and 1978-1979. The negative anomalies in temperature in the latter case lasted through most of the summer of 1979. The corresponding PDSI for the period is shown by the solid curve in Figure 5(c).

We recalculated the PDSI after removing the temperature anomalies by adjusting temperatures to their monthly average values. This adjustment was to single out the contribution of cold temperatures to positive PDSI for the period. The recalculated PDSI is shown by the dashed curve in Figure 5(c). The differences between the solid and dashed curves in Figure 5(c) show that the large precipitation anomalies in summer and autumn 1977 had a dominant effect on PDSI. There was little temperature impact on PDSI under such wet conditions. However, when precipitation was close to normal after the wet period in 1977, temperature effect on the PDSI became significant. In particular, when the negative temperature anomalies were removed in spring and summer of 1979, PDSI changed from an average positive value of 1.5 to an average -1.0 for the months of April-September 1979. This showed that the positive PDSI in the summer months (June-August) had resulted primarily from the cold temperature anomalies in that period. An additional test showed that a temperature anomaly of +2C in the summer months would result in an average value -1.5 PDSI for the period (dotted line in Figure 5(c)). These results illustrate temperature impacts on PDSI. Because such an effect can be significant, it is difficult to decide whether a period of negative PDSI indicates a period of precipitation deficit or warm temperature anomalies.

The temperature effect on the Z-index and, thus, PDSI is shown by consistent changes of monthly Z-index values and temperature in Region 1. Figure 6 shows variations of normalized July precipitation and temperature for the region and Z-index of the same month over the period 1900-1990. There was a significant decrease of the variance of Z-index after 1955 (Figure 6(c)). In the same period, there was a decrease of the variance of July temperature (Figure 6(b)), but an increase of the variance of July precipitation (Figure 6(a)). The Z-index variation shows a behaviour similar to that of monthly temperature variation of the region but not monthly precipitation variation.

GIF -- Three bar graphs: July variations of normalized precipitation, normalized temperature, and z-index over a 90-year period
Figure 6.  Variations of July normalized precipitation (a), temperature (b) and PDSI (c) for Region 1


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