ASSESSING THE PREDICTABILITY OF WEEKLY DROUGHT IMPROVEMENT USING NEBRASKA S AUTOMATED WEATHER DATA NETWORK. By Matthew J. Salerno A MASTER S THESIS

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3 ASSESSING THE PREDICTABILITY OF WEEKLY DROUGHT IMPROVEMENT USING NEBRASKA S AUTOMATED WEATHER DATA NETWORK By Matthew J. Salerno A MASTER S THESIS Submitted to the faculty of the Graduate School of the Creighton University in Partial Fulfillment of the Requirements for the degree of Master of Science, in the Department of Atmospheric Sciences Omaha, NE May,

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5 Abstract For an agricultural state like Nebraska, the economic, environmental, and social impacts of drought are severe. While precipitation is required to reduce drought conditions, the rate of drought improvement varies depending on both total precipitation over an area as well as antecedent soil moisture conditions. The focus of this research was to analyze the response of meteorological variables at surface stations across Nebraska during weeks within a growing season when the Crop Moisture Index, Palmer Z Index, or Palmer Modified Drought Index indicated a positive improvement. Utilizing 55 Automated Weather Data Network (AWDN) stations within eight individual climate divisions, a 15 year climatological dataset of weekly observations, including 12 individual meteorological parameters, was compared with weekly improvements in each drought index. In order to determine how the greatest magnitude of drought index improvement corresponded to each individual station variable, multiple statistical regressions were produced along with corresponding RMSE values from residuals. Results from this study indicated statistically significant correlations between 8 of 12 AWDN variables with the Z index, 6 of 12 AWDN variables with the Crop Moisture Index, and 2 of 12 AWDN variables with the Palmer Modified Drought Index. Additionally, the same statistical regressions were performed on Historical Climate Network (HCN) data and compared to AWDN regression results. The HCN precipitation produced better overall R-values than AWDN precipitation, however AWDN temperature and potential evapotranspiration yielded better overall correlations with each Palmer index. iii

6 Acknowledgements This thesis could not have been completed without the help of my committee members. I would like to thank my advisor, Dr. Jon Schrage, for all your help and support along the way. I appreciate how easy he was to work with and am amazed by how quick and efficient he was in responding to my requests. Dr. Schrage had a lot of responsibility this past year, especially with the state of Creighton Atmospheric Sciences and his move back to Indiana. He helped us students stay focused on our work even through the adversity we faced. Thank you for all your help via Skype, phone, and since you were so far away and I could not have completed my thesis without your expertise. I am equally thankful for having an amazing Department Chair, Dr. Timothy Wagner. He was an excellent professor and supported us graduate students throughout our tenure at Creighton. He is moving to Madison, Wisconsin to begin a new research job and I wish him the best! I would also like to acknowledge Barbara Boustead for your willingness to be on my committee and help me develop a thesis topic even when you were so busy at work and at home caring for your newborn while on leave. You have a knack for climatological research and data interpretation and I greatly appreciated your input. I would also like to take the time to thank the folks at the High Plains Regional Climate Center, especially Ken Hubbard and Natalie Umphlett, who provided me with the data I needed to complete my analyses. I would also like to thank the Drought Mitigation Center staff, specifically Brian Fuchs, for your guidance on websites and articles to utilize. This thesis has been the culmination of my collegiate career and I couldn t have accomplished this feat without the motivation from friends, family, and my faith. iv

7 TABLE OF CONTENTS Abstract... iii Acknowledgments... iv Table of Contents...v List of Figures... vii List of Tables...x List of Acronyms... xii 1. Introduction Background Introduction to the Palmer Drought Severity Index Hydrological accounting of the Palmer Drought Severity Index CAFEC values of the Palmer Drought Severity Index The climatic characteristic of the Palmer Drought Severity Index The Palmer Z Index Calculating the Palmer Drought Severity Index The Palmer Modified Drought Index Limitations of the Palmer Drought Severity Index The Crop Moisture Index Weekly drought index values Methodology Region of study AWDN station network Station precipitation during CMI and Z index transition weeks Drought frequency Predictability of drought improvement Results Panhandle Climate Division...41 v

8 4.2 North Central Climate Division Northeast Climate Division Central Climate Division East Central Climate Division Southwest Climate Division South Central Climate Division Southeast Climate Division AWDN Regressions HCN Regressions Conclusions...88 References...92 vi

9 List of Figures Figure 1. A graph depicting the plotted mean annual weighting factor (K ) for 9 climate divisions based on the driest 12 months in each division as related to moisture demand divided by the moisture supply in each division which is expressed on a logarithmic scale (Palmer, 1965) Figure 2. A climate division map of the CONUS provided by NCDC illustrating the Palmer Z-index categories at each division for June, Figure 3. As in Fig. 2, but for August, Figure 4. A graph representing the summation of monthly Z-index versus length of drought in months. The PDSI (values shown on right vertical axis) categories of extreme, severe, moderate, and mild drought were established based on hand drawn lines using plotted data from random dry periods of varying lengths in the western Kansas and central Iowa climate divisions (Palmer, 1965) Figure 5. A climate division map of the CONUS provided by NCDC illustrating the PDSI categories at each division for June, Figure 6. A Timeline graph of a growing season in North Dakota s climate division 9. The left vertical axis represents the PDSI and PDI index values. The X3 term (established drought) values are represented by squares, the X1 term (wet spell) values are represented by dots, and the PDI is illustrated by the solid line. Crosshatched areas depict index value differences between the PDI and PDSI (Heddinghaus and Sabol, 1991) Figure 7. A climate division map of the CONUS provided by NCDC illustrating the PDI categories at each division for June, Figure 8. A climate division map of the CONUS provided by NCDC illustrating the CMI categories at each division for the week of February 22-28, Figure 9. A generalized soil map of Nebraska provided by the University of Nebraska Lincoln-School of Natural Resources. References to specific soil types can be found at this site: 34 Figure 10. A map of Nebraska s 8 climate divisions including 55 AWDN stations that record soil moisture and 8 other variables. Note that there is no climate division 4 in Nebraska Figure 11. A time series graph of drought and wet periods in the Panhandle division during the period of record January 1999-December The CPC weekly PDI values (left vertical axis) are illustrated by the solid red line. AWDN climate division weekly averaged precipitation (right vertical axis) is represented vii

10 by blue columns. A time versus depth plot of AWDN climate division averaged weekly soil moisture percentage is also provided (bottom) Figure 12. A histogram representing the weekly frequency of PDI drought severity in the Panhandle division during the period of record January December The original Palmer (1965) drought categories were used (mild, moderate, severe, and extreme) Figure 13. A histogram representing the weekly frequency of PDI wetness in the Panhandle division during the period of record January 1999-December The original Palmer (1965) wetness categories were used (slight, moderate, very, and extreme) Figure 14. Nebraska Panhandle division map of AWDN precipitation differences during a two week period when the Palmer Z-index slightly increased from a negative to positive value Figure 15. Nebraska Panhandle division map of AWDN precipitation differences during a two week period when the Palmer Z-index greatly increased from a negative to positive value Figure 16. As in Fig. 11, but for Nebraska s North Central climate division Figure 17. As in Fig. 12, but for Nebraska s North Central climate division Figure 18. As in Fig. 13, but for Nebraska s North Central climate division Figure 19. As in Fig. 14, but for Nebraska s North Central climate division Figure 20. As in Fig. 15, but for Nebraska s North Central climate division Figure 21. As in Fig. 11, but for Nebraska s Northeast climate division Figure 22. As in Fig. 12, but for Nebraska s Northeast climate division Figure 23. As in Fig. 13, but for Nebraska s Northeast climate division Figure 24. As in Fig. 14, but for Nebraska s Northeast climate division Figure 25. As in Fig. 15, but for Nebraska s Northeast climate division Figure 26. As in Fig. 11, but for Nebraska s Central climate division Figure 27. As in Fig. 12, but for Nebraska s Central climate division Figure 28. As in Fig. 13, but for Nebraska s Central climate division Figure 29. As in Fig. 14, but for Nebraska s Central climate division Figure 30. As in Fig. 15, but for Nebraska s Central climate division Figure 31. As in Fig. 11, but for Nebraska s East Central climate division viii

11 Figure 32. As in Fig. 12, but for Nebraska s East Central climate division Figure 33. As in Fig. 13, but for Nebraska s East Central climate division Figure 34. As in Fig. 14, but for Nebraska s East Central climate division Figure 35. As in Fig. 15, but for Nebraska s East Central climate division Figure 36. As in Fig. 11, but for Nebraska s Southwest climate division Figure 37. As in Fig. 12, but for Nebraska s Southwest climate division Figure 38. As in Fig. 13, but for Nebraska s Southwest climate division Figure 39. As in Fig. 14, but for Nebraska s Southwest climate division Figure 40. As in Fig. 15, but for Nebraska s Southwest climate division Figure 41. As in Fig. 11, but for Nebraska s South Central climate division Figure 42. As in Fig. 12, but for Nebraska s South Central climate division Figure 43. As in Fig. 13, but for Nebraska s South Central climate division Figure 44. As in Fig. 14, but for Nebraska s South Central climate division Figure 45. As in Fig. 15, but for Nebraska s South Central climate division Figure 46. As in Fig. 11, but for Nebraska s Southeast climate division Figure 47. As in Fig. 12, but for Nebraska s Southeast climate division Figure 48. As in Fig. 13, but for Nebraska s Southeast climate division Figure 49. As in Fig. 14, but for Nebraska s Southeast climate division Figure 50. As in Fig. 15, but for Nebraska s Southeast climate division ix

12 List of Tables Table 1. The monthly hydrologic accounting illustrated for the years in central Iowa, found in Palmer (1965). The available water capacity of the soil in this division (S) was assumed to include a 1.00 surface layer (S s ) and 9.00 in underlying levels (S u ) Table 2. Long-term means of each hydrologic accounting parameter for 71 years of western Kansas data (top) and 27 years of central Iowa data (bottom), found in Palmer (1965)... 9 Table 3. The monthly climatic coefficients (columns 2-5) for western Kansas and central Iowa (Palmer, 1965) Table 4. An example of moisture departure calculations (column 12) for western Kansas in 1932 (Palmer, 1965) Table 5. An example of monthly weighting factor calculations (row 4) for northwestern North Dakota (Palmer, 1965) Table 6. A selection of random drought periods of varying lengths and the summation of Z index over these periods in western Kansas and Central Iowa (Palmer, 1965) Table 7. The PDSI classes of drought and wetness derived from Fig. 4 (Palmer, 1965) Table 8. An example of the backstepping procedure used to calculate the monthly PDSI, from Alley (1984). The index values depicted here were calculated using Washington, D.C. climate division data from December 1931-December Table 9. The CMI classes of drought and wetness, found in Palmer (1968) Table 10. Equations originally utilized by Palmer (1965) and modified equations used in the CPC weekly Palmer database, found in Rhee and Carbone, Table 11. Correlation coefficients from 96 single variable linear regressions using weekly changes in AWDN data to predict increases in CMI values Table 12. As in Table 11, but for Z index values Table 13. As in Table 11, but for PDI values Table 14. Root Mean Square Error of the CMI calculated by using a random 80% of the AWDN data to predict the remaining 20% Table 15. As in Table 14, but for the Z index Table 16. As in Table 14, but for the PDI x

13 Table 17. Correlation coefficients from 24 single variable linear regressions using weekly changes in HCN data to predict increases in CMI values Table 18. As in Table 17, but for Z index values Table 19. As in Table 177, but for PDI values Table 20. Root Mean Square Error of the CMI calculated by using a random 80% of the HCN data to predict the remaining 20% Table 21. As in Table 20, but for the Z index Table 22. As in Table 20, but for the PDI xi

14 List of Acronyms AWC AWDN CAC CAFEC CMI CONUS COOP CPC E HCN L NCDC NOAA PDI PDSI PE PL PR PRO R RO Z Index Available Water Content Automated Weather Data Network Climate Analysis Center Climatologically Appropriate For Existing Conditions Crop Moisture Index Continental United States Cooperative Observer Network Climate Prediction Center Evapotranspiration U.S. Historical Climate Network Loss National Climatic Data Center National Oceanic and Atmospheric Administration Palmer Modified Drought Index Palmer Drought Severity Index Potential Evapotranspiration Potential Loss Potential Recharge Potential Runoff Recharge Runoff Palmer Moisture Anomaly Index xii

15 1. Introduction Meteorological droughts, or periods of below normal precipitation for prolonged durations, have significant negative impacts on the agricultural industry. During the growing season, farmers rely on precipitation to mitigate the loss of moisture directly from the soil surface and through plants due to evapotranspiration. If drought develops for a period of months or years, decrease in crop yield and water levels in lakes and reservoirs will be detrimental to the food and water supply. Understanding the scientific definitions of drought is the first step in drought monitoring and analysis. Multiple drought definitions have been developed by a variety of user communities, including meteorological, climatological, hydrological, and agricultural definitions (Heim, 2002). Each definition is specific to its community; for example hydrological drought is most commonly used by hydrologists to describe how changes in streamflow impact water supply activities such as hydropower generation, recreation, and irrigation (Heim, 2002). Atmospheric scientists generally prefer the terms meteorological or climatological drought when describing a period of abnormally dry weather. No matter how drought is defined, there is an overall agreement that it is a hazard to many aspects of society. Various quantitative measurements have been developed in the United States, based on the climatological conditions of an area, to categorize the beginning and end of a drought and the level of drought severity (Heim, 2002). Some of the early drought indices established in the early 20th century incorporated a measure of precipitation departure over a given period of time (Heim, 2002). A specific severity of drought was assigned if the amount of precipitation for a series of days fell short of the normal amount for the period. This seems like an intuitive process for quantifying drought, however each drought index 1

16 was useful at a specific location, meaning that a single drought index could not account for the variability in climate from one region to another. By the 1960s Palmer developed the Palmer Drought Severity Index (PDSI) which was one of the first procedures to demonstrate success at quantifying the severity of droughts across different climates (Wells et al. 2004). The PDSI has become one of the relevant drought indices within the climate community. It uses historical precipitation and temperature data to estimate moisture supply and demand within a two-layer soil model (Heim, 2005). Other indices that have been derived from the PDSI including the Palmer Z Index, and the Crop Moisture Index (CMI); these indices will be discussed in detail in the background section of this thesis. This study will utilize the Palmer (1965) indices to evaluate a 15 year history of drought in Nebraska. The state of Nebraska is a favorable region of study due to the range of climates and soil types throughout the state coupled with an extensive spatial network of accurate weather stations which record various data. A weekly Palmer dataset is utilized to capture the fine scale changes in drought conditions; while the PDSI and Z indices are usually calculated monthly, weekly analysis is often required since it provides more detail, identifies the onset of drought more clearly, and allows progressive monitoring of drought conditions (Rhee and Carbone, 2007). Daily station observations will be averaged to weekly values within the eight climate divisions of Nebraska and compared with weekly Palmer index numbers. Single variable linear regressions will be performed to determine which variables produced the greatest changes in index number. 2

17 2. Background 2.1 Introduction to the Palmer Drought Severity Index The PDSI is an index that was developed to characterize classes of drought severity at specific regions on a monthly time scale. The objective for the PDSI was to compare moisture supply to the average absolute moisture requirements of a month (Palmer, 1965). Because it was designated as a meteorological index, moisture supply was defined as the actual measured precipitation that occurred over a specific area and the moisture requirements for the location depend on the local climatology of precipitation, evapotranspiration, soil moisture, and other factors. As a variety of climates exist across the United States, a drought index that is independent of space and time, must include moisture deficits weighted in a manner that can be considered comparable for many areas of study (Palmer, 1965). Palmer originally created his index to compare the moisture deficits in two climatically heterogeneous regions of central Iowa and western Kansas by using monthly averages of temperature and precipitation from surface weather stations. These two regions illustrate why a spatially and temporally independent index is required; a lack of rain during the spring in a moisturerich region like central Iowa would not be as detrimental to agriculture as a similar deficit in western Kansas during the summer months (Palmer, 1965). A monthly time scale was originally applied to the PDSI because most data were available in monthly format and weekly data would have required rigorous calculations that were time consuming. 3

18 2.2 Hydrological accounting of the Palmer Drought Severity Index The initial step in Palmer s computation of the PDSI consisted of producing a monthly hydrologic accounting for 27 years of central Iowa data and 71 years of western Kansas data using multiple parameters related to soil moisture (Heim, 2002). The accounting parameters of evapotranspiration (ET), soil moisture loss (L), recharge (R), and runoff (RO) represented moisture excesses and deficiencies of the soils in each climate division. The complementary potential values, or maximum amount that can occur for a given month, of potential evapotranspiration (PE), potential recharge (PR), potential runoff (PRO), and potential loss (PL) were also calculated. All soil moisture parameters had to be computed using recorded precipitation and temperature data. One of the calculated soil moisture parameters was PE which can be defined as the amount of water evaporated from soil and transpired by a short green crop of uniform height and never short of water (Penman, 1956) and therefore represents the maximum amount of ET that can occur for any given period of time. The PE parameter for the PDSI was determined using the Thornthwaite (1948) equation that estimates the climatic demand for moisture: PE = 1.6 ( 10T I )a (1) where T is the mean monthly temperature (based on a 30 day month and 12 hour days), and a = ( )I 3 ( )I 2 + ( )I I = 12 ( T ai i=12 5 )1.514 (2) 4

19 where I is the heat index that depends on the sum of the mean monthly temperatures(t ai ). Although accounting for PE was based on recorded temperature values, actual ET estimates for the PDSI required assumptions for the available water capacity (AWC) of the soils in the area under consideration (Palmer, 1965). The AWC used for calculating the PDSI was based on a two layer soil model. The upper layer, called the surface soil, was assumed to contain one inch of available moisture at field capacity. The bottom layer varied in depth depending on the root zone for certain plants and the soil characteristics for a given area. Values of AWC that Palmer assigned to soil types in western Kansas and central Iowa totaled six inches and ten inches respectively including the one inch found in the surface layer. ET values were estimated by determining how much of the AWC was depleted at the end of each month which was calculated from the loss term. Soil moisture loss occurred when PE exceeded precipitation at the end of a given month. Loss from the surface soil layer was calculated by the following: L s = S s or (PE P) (3) whichever is smaller, where S s is the available moisture stored in surface layer at beginning of month and P is the total precipitation for the month. It was assumed that moisture loss by PE would occur from the surface layer until all available moisture in this layer was removed (Palmer, 1965). If evaporation continued, then moisture would be removed from the bottom layer. Loss from the underlying soil layer was given by: L u = (PE P L s ) S u AWC, L u S u (4) 5

20 where S u is the available moisture stored in underlying levels at the start of the month, and AWC is the combined available water content for both soil layers (Palmer, 1965). PL was found using Eqns. (3) and (4) above, except the precipitation (P) term was disregarded and L s and L u were replaced by PL s and PL u. By adding L s to L u, the total L was calculated from both soil layers. Monthly ET estimates were computed from L by: ET = (P + L), ET PE. (5) Equation (5) was used only when the surface layer was depleted (that is L exceeded one inch). Otherwise, ET occurred at the potential rate, and ET = PE. The remaining parameters included in the hydrological accounting process were R and RO and their corresponding potential values which depended on precipitation and the AWC. Palmer (1965) assumed that RO occurred when precipitation fell and the full amount of available water was already stored in the soil. Conversely, if one or both soil layers were not at capacity, then a specific amount of precipitation would be needed to recharge the soil, meaning that RO can only occur once precipitation has fulfilled recharge requirements. Monthly RO and R were computed by: RO = (P PE R) (6) R = (P PE RO). (7) An important thing to note is P > PE whenever RO or R occured because the supply of moisture exceeded the demand. PRO was not directly used in the water balance computations, but still needed to be accounted for (Palmer, 1965). PRO can be considered as the maximum amount of RO 6

21 that can occur for a given month. Therefore, it is a good way to measure if actual RO was greater or less than expected especially during months that were normally wetter. The mathematical calculation for PRO that Palmer utilized was: PRO = AWC PR = S (8) where S is the amount of available moisture in both the top and bottom soil layers at the beginning of the month. Another water balance term, PR, was defined as the amount of moisture required to bring the soil to field capacity (Palmer, 1965). It is similar to the other potential values because it measures a maximum condition that could exist (Palmer, 1965). The calculation for PR was: PR = AWC S. (9) Equation (9) describes why PR is small when S is large and vice versa. It also explains the inverse relationship that exists between PR and PRO in Eqn. (8). In Palmer s (1965) hydrologic accounting, the four calculated values related to soil moisture and their four supplemental potential values were applied to a series of months for 27 years of central Iowa data and 71 years of western Kansas data. A representation of the accounting for a few selected years in central Iowa is depicted in Table 1. The year 1935 began with the soil at field capacity and is a good example of how the systematic calculations were carried out. In January, S = AWC and the precipitation that occurred was converted to RO. It was not until April when PE exceeded P and a moisture deficit existed. From Eqn. (3), 0.47 of L occurred which decreased the surface layer to

22 Precipitation exceeded PE in May and returned the surface layer to capacity with 0.47 of R. Once the soil layer was recharged, 1.57 of the precipitation was converted to RO by Eqn. (6). June through September were very dry months because PE greatly exceeded P and S was at its minimum of 2.47 at the end of September. October through December were wetter than normal months contributing to R of the surface layer. Table 1. The monthly hydrologic accounting illustrated for the years in central Iowa, found in Palmer (1965). The available water capacity of the soil in this division (S) was assumed to include a 1.00 surface layer (S s ) and 9.00 in underlying levels (S u ). 8

23 2.3 CAFEC values of the Palmer Drought Severity Index The second step in developing the PDSI involved averaging results from the monthly hydrologic accounting to obtain certain constants or coefficients which were dependent on the climate of a single area of study (Palmer, 1965). Each calculated monthly soil moisture variable including potential runoff and recorded values of temperature and precipitation were averaged for the period of record. The results of the long term monthly means for western Kansas and central Iowa are presented in Table 2. Multiple coefficients were calculated from the mean values by dividing the actual moisture variables by their respective potential terms. These coefficients, called the water balance coefficients, were used to determine monthly moisture departure from normal at each climate division. Table 2. Long-term means of each hydrologic accounting parameter for 71 years of western Kansas data (top) and 27 years of central Iowa data (bottom), found in Palmer (1965). 9

24 To determine monthly moisture departure for a specific climate division, the four potential values were weighted using the water balance coefficients α, β, γ and δ to give the climatically appropriate for existing conditions (CAFEC) quantities (Wells et al, 2004). The water balance coefficients presented in Table 3, columns 2-5, were calculated from the following: α i = ET i PE, i δ i = L i PL, i β i = R i i PR, and γ i = RO i PRO i = RO i, S i where i ranges over the months of the year and a bar over a term indicates an average value (Wells et al, 2004). An example of computed average recharge for March is shown by: L all years L 3 3 = number of years of data. It is important to note that the coefficients were computed using long-term sums rather than from long-term means which accounts for the discrepancies when trying to compute values in Table 3 from Table 2 (Palmer, 1965). Once the water balance coefficients were calculated, they were multiplied by the four potential values to produce monthly CAFEC values. The long-term means of each CAFEC value are equal to the long-term means of the actual values of ET, R, RO, and L in Table 2. 10

25 Table 3. The monthly climatic coefficients (columns 2-5) for western Kansas and central Iowa (Palmer, 1965). For any given month, the CAFEC quantities for evapotranspiration, runoff, recharge, loss, and precipitation were derived from the following: ET = α i (PE) (10) R = β i (PR) (11) RO = γ i (PRO) (12) L = δ i (PL) (13) P = ET + R + RO L. (14) These monthly CAFEC values were compared to actual calculated quantities from the monthly hydrologic accounting to provide a departure from average. For example, if the 11

26 PE was 4.00 for a given August in central Iowa, then ET was (4.00 ) = Therefore, calculated ET needed to be 3.34 in order to satisfy the climatic demand for moisture. Anything above or below this amount would be considered as a departure from what was considered normal or climatically expected for a given August in central Iowa. By combining the soil moisture parameters, the CAFEC precipitation was calculated with Eqn. (14). This is the amount of precipitation that would have maintained the water resources at a level appropriate for the established economic activity of a given area (Palmer, 1965). The CAFEC precipitation was calculated for each individual month and compared to the precipitation that was measured directly. Moisture departure from normal for any given month was provided by: d = P P. (15) Table 4 depicts the CAFEC precipitation, actual precipitation, and the departures (columns 10-12) in western Kansas for consecutive months of Note that June was wetter than normal for the area and each subsequent month was much drier than normal. Table 4. An example of moisture departure calculations (column 12) for western Kansas in 1932 (Palmer, 1965). 12

27 2.4 The climatic characteristic of the Palmer Drought Severity Index The third step in producing the PDSI required conversion of monthly precipitation departures into indices of moisture anomaly using a weighting factor. Straightforward comparisons were unable to be made between values of d because the same departure meant different things at different times and different locations (Wells et al. 2004). To correct for this, a weighting factor was applied to Eqn. (15). Palmer (1965) defined the weighting factor, or climatic characteristic, which was expressed symbolically by K. Initially, the weighting factor was developed by comparing total moisture departures for dry periods of similar lengths in central Iowa and western Kansas. Departures for a 15 month period in central Iowa totaled or per month and departures for a similar period of 14 months in western Kansas totaled or an average of per month (Palmer, 1965). A ratio of the monthly averages of moisture departure between both climate divisions was found by: K Iowa = d Kansas = K Kansas d Iowa = 0.67 where K represents an average climatic characterstic for both areas during these dry periods. Therefore, in order for average monthly moisture departure to be equal for both divisions, the K value in western Kansas needed to be 1.5 times greater than the K value in central Iowa. This suggests that the values of these constants depended on the average moisture shortage of the two places (Palmer, 1965). In order to determine the climate characteristic for each of the 12 months at both climate divisions, Palmer introduced an equation for moisture supply vs. moisture demand. 13

28 Moisture supply was estimated by adding the long-term mean amount of precipitation and loss for any month or period of months. Moisture demand was approximated by adding the long-term mean amount of potential evapotranspiration and recharge that occurred during a month or period of months. The climate characteristic for a single month was a ratio of moisture demand to moisture supply shown by: k = (PE +R ) (P +L ) (16) where k was the first approximation of K and is shown in Table 3, column 6. This was a first approximation because Palmer discovered that k was not adequate in other climate divisions. Palmer realized an adjustment of k was needed in order to create a PDSI that could be compared across many different climates. New monthly climatic characteristic values, denoted by K, were produced by augmenting the first approximation, Eqn. (16). One modification of the initial approximation was the introduction of RO to the moisture demand portion of the equation (PE + R ). Another adjustment to the equation was the implementation of D, which represented the monthly mean of the absolute values of d and was inversely related to K. Empirical constants were also added based on the moisture departures of other climate regions. To achieve a weighting factor that was valid across many climates, other climate divisions besides central Iowa and western Kansas were used in the development of K. A full analysis of nine other U.S. climate divisions yielded monthly values of d for each area. The mean annual K values for each climate division ranged from 1.06 in western Tennessee 14

29 to 1.73 in northwestern North Dakota and are displayed in Fig. 1 (Palmer, 1965). These values were based on the driest 12 month periods in each division. From Fig. 1, the monthly weighting factor K was developed for each climate division and was given by: K = 1.5log 10 [( PE +R +RO P +L +2.8 D )] (17) where the bars over each term represent the mean value for each of the 12 calendar months. A sample of K values for a selected climate division is illustrated in Table 5. K was included in the final calculation of K which is given by: K = K (18) 1 D K where is an empirical constant that was derived by taking the average of all annual sums of D K for the 9 climate divisions. An example of calculating K for January in the northwestern North Dakota climate division in Table 5 is shown below: K = (2.42) = Overall, the K values established reasonable comparability between different climates (Palmer, 1965). By incorporating a variety of climate divisions, Palmer was able to improve the original climatic characteristic and derive Eqns. (17) and (18). These monthly weighting factors ultimately contributed to the finalization of the PDSI. 15

30 Table 5. An example of monthly weighting factor calculations (row 4) for northwestern North Dakota (Palmer, 1965). Figure 1. A graph depicting the plotted mean annual weighting factor (K ) for 9 climate divisions based on the driest 12 months in each division as related to moisture demand divided by the moisture supply in each division which is expressed on a logarithmic scale (Palmer, 1965). 16

31 2.5 The Palmer Z Index The fourth step in constructing the PDSI was converting moisture departures into a monthly index known as the Z index, or moisture anomaly index, using the derived climatic characteristic values. The Z index was defined mathematically as: z = dk (19) where z is a non-dimensional index of the weighted monthly moisture departures. Each value of z represents the departure of weather for any particular month from the average moisture climate of that month and is applicable to any climate division (Palmer, 1965). Palmer applied the Z index to the western Kansas and Central Iowa data. By analyzing certain months in the period of record, common trends were discovered. It was noted that most of the greatest negative moisture anomalies occurred during the summer months when the weather became hot and dry. Conversely, large negative values of Z index were not often produced during the winter months due to lower demand for precipitation. Unsurprisingly, very wet months occurred during the period of record at both locations, which were indicated by index values over Palmer categorized both drought and wet periods into four arbitrary classes: mild, moderate, severe, and extreme. The Z index was originally established for western Kansas and central Iowa, but has since been introduced in other climate divisions to indicate moisture conditions over a particular wet or dry month in the middle of a longer duration drought or wet period (Karl, 1986). The Z index is recorded each month at all 344 climate divisions within the Continental United States (CONUS). NCDC produces updated monthly maps dating back to An example of the Z index map for June, 2014 is provided in Fig. 2. June,

32 included drastic differences in category values between extreme drought conditions in the southwest and extremely moist conditions throughout north central United States. By August, 2014, shown in Fig. 3, drought conditions were ameliorated over parts of the southwest and California and severe to extreme drought had developed in portions of the southeast. The transition of Z index anomalies from June to August 2014 indicates drastic changes in moisture conditions over a three month period. Figure 2. A climate division map of the CONUS provided by NCDC illustrating the Palmer Z-index categories at each division for June, Figure 3. As in Fig. 2, but for August,

33 2.6 Calculating the Palmer Drought Severity Index The fifth and final step in formulating the PDSI was to calculate drought severity and establish criteria to signify the beginning and ending of drought periods (Palmer, 1965). Drought severity was determined by observed changes in the Z index over many months when values were consistently negative. The driest consecutive months for the period of record in northern Kansas and central Iowa were used to develop thresholds for each category of drought severity. Once each drought category was established, initiation and termination of droughts could be calculated. The categories of drought severity that Palmer defined were based on some of the driest periods in western Kansas and central Iowa. The monthly sums of the Z index during these dry intervals are shown in Table 6. The accumulated Z index values were then plotted on Fig. 4 and a line of fit was drawn to represent the extreme drought threshold. The horizontal line at the top of Fig. 4 represented normal conditions when the accumulated monthly Z index was zero. Between the extreme drought and normal condition lines, the moderate and severe levels were also drawn in at equal lengths (Palmer, 1965). The threshold values for each drought category were -4.0 for extreme, -3.0 for severe, -2.0 for moderate, and -1.0 for mild. An equation to approximate the level of drought severity was developed from Fig. 4 and was given by: X i = i t=i Z t /(0.309t ) (20) where t is the number of consecutive months in a dry spell and Z t is the sum of the Z index for the period. Equation (20) represented the first approximation of the PDSI. 19

34 Table 6. A selection of random drought periods of varying lengths and the summation of Z index over these periods in western Kansas and Central Iowa (Palmer, 1965). Figure 4. A graph representing the summation of monthly Z-index versus length of drought in months. The PDSI (values shown on right vertical axis) categories of extreme, severe, moderate, and mild drought were established based on hand drawn lines using plotted data from random dry periods of varying lengths in the western Kansas and central Iowa climate divisions (Palmer, 1965). 20

35 The first approximation of the PDSI was reevaluated because the cumulative procedure for measuring drought severity was misleading (Palmer, 1965). During a series of very dry months there may exist an anomalously wet month which would impact the total summation of Z values and decrease the overall severity. This is problematic because a drought that would otherwise be extreme might be discounted. Palmer cited an example of a very wet month, August 1933, in the midst of a severe drought which caused the cumulative Z index to appear less serious. To account for this problem, an adjustment to the cumulative method was made. Instead of a cumulative sum of monthly Z index values, Palmer developed an increment based method for the PDSI where each consecutive month was evaluated individually in terms of its influence on the level of drought severity. The initial month of drought was determined by substituting i = 1 and t = 1into Eqn. (20) to yield: X 1 = Z 1 /3. (21) Successive drought months can be calculated by adding an extra term to Eqn. (21): X i = (Z i /3) + cx i 1 (22) where X i = X i X i 1. The terms X i and X i 1 are drought index values for month i and the previous month respectively. The constant c in Eqn. (22) was derived by plugging in computed values of Z i from two arbitrary values of X i 1 and t when X i was zero. A final version of the PDSI used to compute monthly contributions to drought severity (Palmer, 1965) was given by: X i = (Z i /3) X i 1. (23) 21

36 The (Z i /3) term represents the current month s moisture anomaly and the 0.897X i 1 term characterizes the memory component, or influence of drought conditions from previous months on the current level of drought (Heim, 2005). The PDSI is not only used to determine droughts, as it can also be applied to wet periods, or consecutive months when the departure term is positive. A positive monthly departure implies wetter than normal conditions and causes the Z index value to be positive. This results in a PDSI value that is positive and a severity of wetness can then be evaluated. The categories of wetness that Palmer (1965) defined were similar in nature to the drought classes and included insipient wet spell, slightly wet, moderately wet, very wet, and extremely wet. The PDSI threshold values for both dry and wet categories are illustrated in Table 7. Inclusion of these wet classes provided the ability to determine the transition of drought to wet periods and vice versa. Table 7. The PDSI classes of drought and wetness derived from Fig. 4 (Palmer, 1965). 22

37 When drought conditions are mitigated by normal or above normal precipitation, Eqn. (20) will eventually reach zero (Palmer, 1965). However, this was too strict of a requirement to decide whether or not a drought ended. Therefore, the beginning and ending of a drought had to be calculated using a complex back stepping procedure. Palmer assumed that drought would be terminated when the PDSI approached neutral conditions or Similarly, an established wet spell definitely ended when the PDSI dropped to the near normal category of To determine the amount of moisture surplus or deficit required to bring the PDSI to neutral conditions, three index values were defined: X 1 for severity index of a wet spell that is being established, X 2 for severity index of a drought that is being established, and X 3 for severity index of any drought or wet spell that has already been established. By definition, variable X 1 must always be positive and variable X 2 must always be negative. However, if Eqn. (20) was to violate these rules, the variables X 1 and X 2 were set equal to zero. Drought was considered to be established when X after a previous drought or wet spell ended and a wet spell was established when X after a previous drought or wet spell was terminated (Alley, 1984). Both of these conditions caused X 3 = X 1 or X 3 = X 2 signifying that a wet or dry spell had been established. Once each drought or wet spell returned to the near normal category, X 3 was reset to zero. The amount of moisture required to either increase or reduce the PDSI to nearnormal conditions was calculated using the monthly Z index and a new Z index value, Z e. The cessation of an established drought occurred when the Z index value for a given month was greater than Z e where: 23

38 Z e = 2.691X 3i (24) This would reduce the severity of an established drought to Comparably, the ending of an established wet spell occurred when the Z index value for a given month was less than Z e, but in this case, Z e was: Z e = 2.691X 3i (25) This would force the severity level of a given wet spell to return to Both Eqns. (24) and (25) were derived by solving for Z i in Eqn. (23) and substituting or 0.50 for X i (Alley, 1984). To predict whether an established drought or wet spell would end, Palmer relied on a percentage of probability method. The formula for percentage probability was given by: P e = j=j j=0 U i j j=j Z e + j=1 U i j 100% (26) where U = Z in a drought and U = Z 0.15 in a wet spell for the month being considered, j indicates the number of preceding months, and j is the first month of the current drought or wet spell (Palmer, 1965). From Eqn. (26), a drought or wet spell was identified to be definitively over when the probability reached 100%. However, using a back stepping procedure, the drought or wet period was considered to end during the first month when P e was greater than 0% and remained above 0% until it attained a value of 100% (Karl, 1986). For example, if P e was 0, 10, 50, and 100% over four consecutive months, the drought or wet period would have ended at the second month in the series when P e = 10%. 24

39 One of the drought index terms X1, X2, or X3 was chosen to represent the PDSI value for a given month using the back stepping method. The term selected depended on the probability that an established drought or wet period had ended (Heim, 2002). Palmer designed a set of rules on which index should be chosen by computing X1, X2, and X3 over many months and then working backward depending on how the weather changed each month. Table 8 depicts an example of the back stepping procedure for a given series of months. The P e increased from 0 to 100% from December 1931 to November Initially, values for X were not calculated until P e reached 100% in November The values for X were filled in using the backtracking method from November 1932 through January 1931 which incorporated the following rules: 1) assign X = X 1 until X 1 = 0, 2) assign X = X 2 until X 2 = 0, 3) repeat steps 1 and 2 until a month was reached that already had an X value assigned (Alley, 1984). If the established drought in December 1931 had continued through November 1932, the probability of the drought ending would have been zero and X = X 3 for each month. The back stepping method can be applied to any period of record to produce monthly values of PDSI. However, it is important to note that this procedure to determine the ending of drought or wet spells cannot be adequately used for real-time calculations of the PDSI (Heim, 2002). Therefore, the PDSI was originally developed as an index that was not meant to be used operationally. An operational version of the PDSI was eventually introduced by the Climate Analysis Center (CAC) to avoid the back stepping procedure. The values of the operational PDSI were set to X 3 whenever 0% < P e 50%, and X 1 or 25

40 X 2, depending on which had the opposite sign of X 3, whenever 50% < P e 100%. Like the Z index, NCDC produces monthly maps of the PDSI dating back to 1900 for all 344 climate divisions. An example of the PDSI map for June, 2014 is illustrated in Fig. 5. Table 8. An example of the backstepping procedure used to calculate the monthly PDSI, from Alley (1984). The index values depicted here were calculated using Washington, D.C. climate division data from December 1931-December Figure 5. A climate division map of the CONUS provided by NCDC illustrating the PDSI categories at each division for June,

41 2.7 The Palmer Modified Drought Index The Palmer modified drought index (PMDI) or (PDI) is an improved operational version of the PDSI that was produced by Heddinghaus and Sabol (1991). During drought improvement, the PDI uses the sum of the wet spell and established drought terms (X 1 and X 3 ) after they have been weighted by their probabilities to determine the index value for a given month. This method eliminated having to flip between positive and negative PDSI values whenever the probability crossed the 50% threshold (Heddinghaus and Sabol, 1991). PDSI and PDI values differed only during transition periods when a drought or wet period was becoming established or declining. Otherwise both the PDSI and PDI were the same when P e = 0% or 100%. Heddinghaus and Sabol (1991) described the PDI to be more continuous and more likely to be normally distributed than the PDSI. A transition period from extreme drought to normal weather in North Dakota s climate division 9 was cited as an example of the PDI s usefulness. Figure 6 depicts the differences between the PDSI and PDI as drought recovery occurred from week 28 thru 51. Note how the PDSI is initially less than the PDI until week 43 when the PDSI begins to fluctuate between positive and negative values while the PDI remains negative and gradually returns to the near-normal category. After being received favorably by the NCDC, the PDI was introduced as a drought monitoring product in It is currently available as a standalone product for all 344 climate divisions in the CONUS. An example of the PDI map for June, 2014 is illustrated in Fig. 7. Slight differences in divisional values can be identified when comparing Fig. 5 to Fig. 7 i.e. Florida panhandle, north central New Mexico, and northeastern Iowa, but the PDSI and PDI maps are generally in agreement each month. 27

42 Figure 6. A Timeline graph of a growing season in North Dakota s climate division 9. The left vertical axis represents the PDSI and PDI index values. The X3 term (established drought) values are represented by squares, the X1 term (wet spell) values are represented by dots, and the PDI is illustrated by the solid line. Crosshatched areas depict index value differences between the PDI and PDSI (Heddinghaus and Sabol, 1991). Figure 7. A climate division map of the CONUS provided by NCDC illustrating the PDI categories at each division for June,

43 2.8 Limitations of the Palmer Drought Severity Index The PDSI has been a major influence on the development of other drought indices, but it also has many drawbacks. Limitations of the PDSI have been summarized by Alley (1984), Karl and Knight (1985), and Headdinghaus and Sabol (1991). Problems associated with the PDSI are related to the hydrologic accounting and the assumptions that Palmer (1965) made during the development of the PDSI. Alley (1984) documented defects in Palmer s universal water balance model. Changes in vegetation and root development over many seasons were not taken into account when measuring values such as evapotranspiration and soil moisture at each climate division. Also, the assumption of a one inch upper soil layer depth turned out to be too small of a capacity in some climates. The one inch moisture capacity of the surface layer was often small compared to monthly values of moisture loss that occurred causing moisture storage in the upper layer to go from full to empty in a single month (Alley, 1984). The water balance computations were therefore insensitive to the inclusion of the surface layer. Alley (1984) also mentioned that the most serious flaw in the water balance computations was the estimation of runoff. Runoff in the hydrologic accounting was dependent on soil moisture recharge and no lag was incorporated in the model to account for the time it took excess water to appear as runoff. By not introducing lag into the model, overestimations of runoff during the initial month were introduced. Alley (1984) described shortcomings of the hydrologic accounting, but other drawbacks included assumptions that were made in development of the PDSI. 29

44 The sensitivity of the PDSI to many of its assumptions was noted by Karl and Knight (1985) and Heddinghaus and Sabol (1991). Snow coverage was not included in the model and all precipitation was assumed to fall as rain (Karl and Knight, 1985). This caused issues with the timing of large or small Z and PDSI values during the winter and early spring months when the ground was still frozen. Other issues with the PDSI were the definition of each drought category and the weighting factor. The index used arbitrary rules to qualitatively define each drought and wet period category and droughts were assumed to end when the index reached a subjective value of Palmer (1965) made the assumption that K would allow comparison of the PDSI between many types of climates. However, the climate characteristic, or weighting factor was found to be weekly justified and inaccurate for extreme climates because it was based on a limited amount of comparisons. Despite all of the weaknesses mentioned above, the PDSI has become wellrecognized and users are familiar with its utility. It will continue to serve as a stand-alone drought monitoring product. Ultimately, the PDSI has contributed to the expansion of other drought indices such as the Crop Moisture Index (CMI). 30

45 2.9 The Crop Moisture Index Palmer introduced the CMI as another drought monitoring tool following completion of the PDSI. The CMI is used to analyze short-term moisture conditions affecting crops (Keyantash and Dracup, 2002). Computation of the CMI requires weekly values of temperature and precipitation at weather stations in each climate division. Much like the PDSI, the CMI uses temperature to estimate potential evapotranspiration by means of Thornthwaite s method. The CMI also uses the same two layer soil model as the PDSI to compute the weekly hydrologic accounting (Hill, 1974). To represent moisture demand, calculated evapotranspiration is compared to the expected value for a given week and expressed as an anomaly of evapotranspiration (Hill, 1974). Recorded precipitation was used to calculate values or recharge and runoff which represent moisture supply. The recharge and runoff values are combined into a separate wetness index and added to the evapotranspiration anomaly to obtain the weekly CMI (Hill, 1974). The CMI is currently recorded at each of the 344 climate divisions on a weekly basis and is included in the Weekly Weather and Crop Bulletin published by the U.S. Department of Agriculture during a growing season. Palmer (1968) established categories for the CMI that relate to crop and soil moisture conditions. These categories are depicted in Table 9. The CMI is not intended to assess long-term drought and thus maps of the current week are available through the U.S. Drought Portal and CPC. An example of the climate division CMI map for the week of February 22-28, 2015 is illustrated in Fig. 8. The southeastern U.S. was abnormally moist to excessively wet during this period whereas most the remaining climate divisions experienced near normal moisture conditions. 31

46 Table 9. The CMI classes of drought and wetness, found in Palmer (1968). Figure 8. A climate division map of the CONUS provided by NCDC illustrating the CMI categories at each division for the week of February 22-28,

47 2.10 Weekly drought index values The PDSI and Z index were originally designed to be calculated monthly, though Palmer mentioned in his original manuscript that weekly analysis of these indices was also plausible. Palmer suggested a method of calculating PDSI values for 52 weeks using weekly constants and equations that are derived from monthly constants and equations. This weekly monitoring method has been adopted for operational use by the National Oceanic and Atmospheric Administration (NOAA) National Weather Service (NWS) Climate Prediction Center (CPC) (Rhee and Carbone, 2007). The CPC provides weekly PDSI values at each climate division. For weekly analysis, the coefficients derived in Eqn. (26) were modified and are depicted in Table 10. Weekly CAFEC coefficients and the climate characteristic K were derived from monthly values using amplitudes and phases of six harmonics for each coefficient, and the coefficients β and γ were divided by 4.35 to normalize between weekly and monthly time scales (Rhee and Carbone, 2007). The PDSI values are computed for weeks ending on Saturday and calculations are reinitiated each year on the first Wednesday of March and are continued until the first Wednesday of March the following year (Rhee and Carbone, 2007). In conjunction with the PDSI, the CPC also computes the Z index, PMDI, and CMI for all 52 weeks of the year for a period of record from 1885 to the current year (see ftp://ftp.ncdc.noaa.gov/pub/data/cirs/climdiv/divisional-readme.txt). Table 10. Equations originally utilized by Palmer (1965) and modified equations used in the CPC weekly Palmer database, found in Rhee and Carbone,

48 3. Methodology 3.1 Region of study The purpose of this research was to analyze a 15 year history of droughts and wet periods from January 1999 thru December 2013 in Nebraska s eight climate divisions. Nebraska was selected because it contains climates similar to Palmer s original study regions of central Iowa and western Kansas. The climate of Nebraska varies from semiarid in the west to sub humid in the east (Coop et al., 2014). For comparison, average weekly precipitation from this study s 15 year dataset was 0.26 in Nebraska s panhandle climate division and 0.43 in Nebraska s east central climate division. Nebraska contains a variety of soil types. A generalized soil map is provided for reference in Fig. 9. Soils range from clay and silt in the eastern half of the state (blues and purples) to sandy in northern and western parts of the state (yellows and greens). The clay and silt soils prevent deep moisture seepage because they consist of fine compacted particles whereas soils that are sandy in nature consist of larger particles and allow deeper moisture penetration. Therefore, the AWC varies within Nebraska s climatic divisions. Figure 9. A generalized soil map of Nebraska provided by the University of Nebraska Lincoln-School of Natural Resources. References to specific soil types can be found at this site: 34

49 3.2 AWDN station network This research utilized the AWDN which was implemented by the University of Nebraska in 1981 to support agricultural activity (Coop et al., 2014). There are currently 67 operational stations within Nebraska s eight climate divisions including 55 stations that support soil moisture measurements. AWDN weather stations record hourly and daily air temperature, soil temperature, relative humidity, wind speed, solar radiation, precipitation, and soil water content at four individual depths. Daily station values were provided by the High Plains Regional Climate Center (HPRCC) and were averaged to a weekly time scale in order to make direct comparisons with the weekly CPC Palmer dataset. The 55 stations used in this study are illustrated in Fig. 10. The AWDN was selected over the HCN because of its higher spatial accuracy with temperature data (Coop et al., 2014) and a larger variety of recorded variables. The AWDN stations are automated and record 12 individual parameters using a variety of instruments. Air temperature and relative humidity are recorded at a height of 1.5 m using a thermistor temperature sensor and humi-cap relative humidity sensor that are stored inside a shielded box and connected to a data logger. The soil temperature probe is encased in an aluminum tube painted white (Blauvelt, AWDN Maintenance Manual) and records temperature at a depth of 10 cm. Wind speed is recorded via a Met-One cup anemometer at a height of 3.0 m. Precipitation is measured from an electronic tipping bucket style rain gauge set at a height of 0.5 m-1.0 m. Soil moisture is recorded with Theta or Vitel probes that are set at 10 cm, 25 cm, 50 cm, and 100 cm depths and are calibrated to soil type at each layer (sand, silt, or clay). Global solar radiation over a 24 hr. period is 35

50 logged using a pyranometer at a height of 2.0 m. Potential evapotranspiration is calculated using the daily Penman equation: (R +γ n G) + γ f(u +γ 2)(e s e a ) (27) where = change in humidity with air temperature, γ= psychrometric constant, R n = net radiation estimated from global solar radiation, G= heat flux in soil estimated as zero, e s = saturated vapor pressure, e a = actual vapor pressure, f(u 2 ) = W and W = daily wind run over a reference crop of alfalfa. Information on all instrumentation can be found here ( Figure 10. A map of Nebraska s 8 climate divisions including 55 AWDN stations that record soil moisture and 8 additional variables. Note that there is no climate division 4 in Nebraska. 36

51 3.3 Station Precipitation during CMI and Z index transition weeks Transition weeks from droughts to neutral conditions or wet periods were evaluated at each climate division in Nebraska. Weekly changes in recorded precipitation at all AWDN stations within a climate division were compared to increases from negative to positive CMI or Z index values. Large and small CMI and Z index transition weeks were chosen from the CPC dataset. Changes in precipitation at each AWDN station were compared to changes in both the CMI and Z index values to determine if there was an analogous relationship. The CMI and Z index were preferred over the PDI for this portion of the analysis because two week transition periods were used. Changes in the PDI respond slower in most instances to short-term moisture anomalies because any week s value is dependent on accumulated moisture departures from the first week of a growing season (first week in March for the CPC dataset). The CMI and Z index respond much more rapidly to weekly changes in drought or wet conditions because the current week s value depends on the moisture conditions from the previous week and previous month respectively. Precipitation was compared to the CMI and Z index during transition periods. Precipitation was favored over the other AWDN variables because it represents moisture supply in the CMI and Z index calculations. Increases in precipitation amounts from one week to the next typically promoted a corresponding increase in the CMI and Z index. The change in precipitation needed to bring the CMI or Z index out of a drought and into a neutral or wet category for selected weeks was plotted at each individual AWDN station using ArcMap

52 3.4 Drought frequency Classes of drought severity were applied to each climate division PDI value for this study s 15 year dataset. PDI drought severity was determined using the same categories as Palmer s original study (see Table 7). Negative weekly PDI values for the period of record were assigned a severity level and drought frequency graphs were generated. Drought frequency was quantified as the number of times the PDI reached a specific level of drought (i.e. mild drought -1 < PDI < -2) for any individual week in the 15 year period. These graphs were produced for each of the eight climate divisions and illustrated the seasonality of annual drought severity. Excessive wetness was also classified at each climate division for the 15 year period of record. PDI wetness was evaluated using the same categories as Palmer s original study (see Table 7). Positive weekly PDI values in the dataset were assigned a level of wetness and wetness frequency graphs were created. Wetness frequency was quantified as the number of times the PDI reached a specific level of wetness (i.e. slightly wet 1 < PDI < 2) for any individual week in the 15 year period. These graphs were produced for each of the eight climate divisions and illustrated the seasonality of annual excessive wetness. 38

53 3.5 Predictability of drought improvement Single variable linear regressions were performed to analyze the predictability of the PDI, CMI, and Z index at each climate division. Changes in weekly AWDN station data were compared to corresponding drought weeks where each index value signified a positive increase. Correlations between each drought index and station variable were determined by the statistical significance of R-values. Each regression was set up using AWDN station data as X predictor values (independent) and the CMI, PDI, or Z index as Y values that were being predicted or explained (dependent). Once each of the residual data points were graphed, a fit line was added, and the correlation coefficient (R-value) was determined. A trend in the data was considered as real and significant if the null hypothesis could be rejected. In order to reject the null hypothesis, a confidence level of 95% was chosen, and any regressions with P- values less than 0.05 were considered statistically significant. Multiple criteria were introduced to the regression procedure in order to attain statistically significant R-values. The first criterion required the PDI, CMI, and Z index to be in an established drought which was defined as a period of at least three weeks with an index value below zero. The second criterion entailed drought index improvement from one week to the next; therefore only positive changes were used. The third criterion was a defined growing season threshold from March 1-November 18 to reduce the influence of frozen soil or precipitation. The final criterion included the removal of improvement weeks when changes in soil moisture or precipitation were 0.00 and suspect data that resulted from averaging weeks with missing values or measurements that seemed irregular. 39

54 The regression analysis was completed for each of the eight climate divisions in Nebraska. After correlations were produced for all of the 12 AWDN variables, additional regressions were executed for the HCN variables. The HCN variables of precipitation, average temperature, and potential evapotranspiration calculations using Thornthwaite s method were included as part of the weekly CPC dataset and were averaged for each climate division for use in the weekly PDI. Regression R-values from the HCN were compared to R-values from the AWDN to determine whether AWDN station variables had stronger or weaker correlations. To provide a sense of the predictive value of the results obtained from the regressions performed, a second analysis of the dataset was implemented for every climate division. For each pair of independent and dependent random variables (such as AWDN or HCN data and the corresponding drought indices), a subsample of 80% of the available weeks was chosen randomly. Based on this subsample, regression parameters were recomputed as had been done originally for the full 100% of the available weeks; these new regression parameters were then used to formulate a linear model and predict the values of the dependent variable for the remained 20% of the weeks. The root mean square error (RMSE) was then calculated using residuals from the predicted data (20%). The RMSE explains the error found between observed and modeled changes in Palmer index values made by station data. 40

55 4. Results 4.1 Panhandle Climate Division The Panhandle climate division experienced annual variability in precipitation and soil moisture during the period of record According to AWDN precipitation, dry years included , , and 2012; wet years included 1999, , and The Panhandle division was in a drought period (PDI<-1) 51% of the time and in a wet spell (PDI>1) 21% of the time. The average weekly AWDN soil moisture depicted in Fig. 11 was regularly low (below 15%) at each layer for the majority of the record. Soil moisture recharge was most apparent after major precipitation events. Large increases in soil moisture transpired during the spring weeks of 2001, 2005, 2009, and 2010 (Fig. 11). The frequency of droughts and wet periods are depicted in Fig. 12 and 13. A substantial amount of severe to extreme droughts occurred during the summer months including a single week in July that experienced eleven separate occasions of PDI values below -4. Weeks of very wet to extreme wetness occurred most often during the summer and fall months including two weeks in June and October that accounted for 4 separate occasions of PDI values above 4. There was an overall higher frequency of PDI weeks in the dry category than wet category in the Panhandle division. Improvement weeks where the Z index increased from a negative to positive value effectively ending a drought are illustrated in Fig. 14 and 15. AWDN precipitation increased by less than 0.35 at all six stations during a small Z index transition of 0.75 (Fig. 14). AWDN precipitation increased by over an inch at the far western stations, but decreased at two stations during a large Z index transition of 3.09 (Fig. 15). 41

56 Figure 11. A time series graph of drought and wet periods in the Panhandle division during the period of record January 1999-December The CPC weekly PDI values (left vertical axis) are illustrated by the solid red line. AWDN climate division weekly averaged precipitation (right vertical axis) is represented by blue columns. A time versus depth plot of AWDN climate division averaged weekly soil moisture percentage is also provided (bottom). 42

57 Figure 12. A histogram representing the weekly frequency of PDI drought severity in the Panhandle division during the period of record January 1999-December The original Palmer (1965) drought categories were used (mild, moderate, severe, and extreme). Figure 13. A histogram representing the weekly frequency of PDI wetness in the Panhandle division during the period of record January 1999-December The original Palmer (1965) wetness categories were used (slight, moderate, very, and extreme). 43

58 Figure 14. Nebraska Panhandle division map of AWDN precipitation differences during a two week period when the Palmer Z-index slightly increased from a negative to positive value. Figure 15. Nebraska Panhandle division map of AWDN precipitation differences during a two week period when the Palmer Z-index greatly increased from a negative to positive value. 44

59 4.2 North Central Climate Division The North Central climate division experienced fluctuating precipitation and soil moisture conditions during the period of record Represented by precipitation, dry years included 2000, , 2006, 2009, and 2012; wet years included 1999, 2001, 2005, , , and The North Central division was in a drought period (PDI<-1) 37% of the time and in a wet spell (PDI>1) 43% of the time. The average weekly AWDN soil moisture depicted in Fig. 16 ranged from 0.17% to 32% at all depths. Soil moisture recharge was most noticeable after major precipitation events. Increases in soil moisture were most prominent during spring of 2001 and summer of 2010 (Fig. 16). The frequency of droughts and wet periods are depicted in Fig. 17 and 18. Severe to extreme droughts occurred often during weeks in the summer and fall months from May- September. Weeks of very wet to extreme wetness were most frequent during the spring and winter months including weeks in April and May that recorded PDI values above four on nine separate occasions. There was a higher overall frequency of PDI weeks in the wet category than dry category in the North Central division. Improvement weeks where the Z index increased from a negative to positive value effectively ending a drought are illustrated in Fig. 19 and 20. AWDN precipitation increased considerably at some locations (2.27 and 3.10 ) and decreased at other locations (-1.20, ) during a Z index improvement of 0.54 (Fig. 19). AWDN precipitation increased considerably over the eastern half of the division during a large Z index transition of 3.40 (Fig. 20). 45

60 Figure 16. As in Figure 11, but for Nebraska s North Central climate division. 46

61 Figure 17. As in Figure 12, but for Nebraska s North Central climate division. Figure 18. As in Figure 13, but for Nebraska s North Central climate division. 47

62 Figure 19. As in Figure 14, but for Nebraska s North Central climate division. Figure 20. As in Figure 15, but for Nebraska s North Central climate division. 48

63 4.3 Northeast Climate Division The Northeast climate division experienced annual changes in precipitation and soil moisture conditions throughout the period of record Based on precipitation, dry years included 2000, 2002, 2006, and 2012; wet years included 1999, 2001, , , and The Northeast division was in a drought period (PDI<-1) 22% of the time and in a wet spell (PDI>1) 52% of the time. The average weekly AWDN soil moisture depicted in Fig. 21 was consistently high (above 20%) for the period of record. Soil moisture recharge was most noticeable after major precipitation events. The most prevalent increases in soil moisture occurred in spring and summer weeks of (Fig. 21). The frequency of droughts and wet periods are depicted in Fig. 22 and 23. Severe to extreme droughts occurred most often during a series weeks in July and September. Weeks of very wet to extreme wetness were most frequent during the spring, fall, and winter months including weeks in April, October, and December that recorded PDI values above four on nine or ten separate occasions. There was a higher overall frequency of PDI weeks in the wet category than dry category in the Northeast division. Improvement weeks where the Z index increased from a negative to positive value effectively ending a drought are illustrated in Fig. 24 and 25. AWDN precipitation increased considerably at the western stations (1.28 and 1.93 ) and slightly increased at the eastern stations (0.03, 0.67 ) during a small Z index transition of 0.65 (Fig. 24). AWDN precipitation significantly increased at two of the four stations (1.95, 3.15 ) during a large Z index transition of 3.69 (Fig. 25). 49

64 Figure 21. As in Figure 11, but for Nebraska s Northeast climate division. 50

65 Figure 22. As in Figure 12, but for Nebraska s Northeast climate division. Figure 23. As in Figure 13, but for Nebraska s Northeast climate division. 51

66 Figure 24. As in Figure 14, but for Nebraska s Northeast climate division. Figure 25. As in Figure 15, but for Nebraska s Northeast climate division. 52

67 4.4 Central Climate Division The Central climate division experienced variability in precipitation and soil moisture conditions throughout the period of record According to precipitation, dry years included 2000, , 2006, 2009 and 2012; wet years included 1999, 2001, 2005, , and The Central division was in a drought period (PDI<-1) 43% of the time and in a wet spell (PDI>1) 43% of the time. The average weekly AWDN soil moisture depicted in Fig. 26 ranged from 0.5% to 40% for all layers throughout the period of record. Soil moisture recharge was most noticeable after major precipitation events. The highest increases in soil moisture were during the summer and fall weeks of 2001, and the spring and summer weeks of 2003, and 2005 (Fig. 26). The frequency of droughts and wet periods are depicted in Fig. 27 and 28. Severe to extreme droughts were most frequent during weeks in June, July, and August including a series of weeks with recorded PDI values below -4 on eight separate occasions. Weeks of very wet to extreme wetness were most numerous in April, May, and June. The total frequency of drought and wet weeks in the Central division was nearly equal (334 vs 336). Improvement weeks where the Z index increased from a negative to positive value effectively ending a drought are illustrated in Fig. 29 and 30. AWDN precipitation increased significantly at the western stations (1.12 and 0.91 ) and decreased slightly at two of the southern stations (-0.18, ) during a small Z index transition of 0.52 (Fig. 29). AWDN precipitation increased by 1.00 or greater at most stations during a large Z index transition of 3.61 (Fig. 30). 53

68 Figure 26. As in Figure 11, but for Nebraska s Central climate division. 54

69 Figure 27. As in Figure 12, but for Nebraska s Central climate division. Figure 28. As in Figure 13, but for Nebraska s Central climate division. 55

70 Figure 29. As in Figure 14, but for Nebraska s Central climate division. Figure 30. As in Figure 15, but for Nebraska s Central climate division. 56

71 4.5 East Central Climate Division The East Central climate division experienced variable precipitation and soil moisture conditions throughout the period of record Determined by precipitation, dry years included 2000, , 2009 and ; wet years included 1999, , , and The East Central division was in a drought period (PDI<-1) 38% of the time and in a wet spell (PDI>1) 35% of the time. The average weekly AWDN soil moisture depicted in Fig. 31 was ordinarily high (above 20%) at all layers throughout the period of record. Soil moisture recharge was most noticeable after major precipitation events. The greatest increases in soil moisture occurred in the summer weeks of 2007, 2011, and spring of 2006 and 2013 (Fig. 31). The frequency of droughts and wet periods are illustrated in Fig. 32 and 33. Severe to extreme droughts were most frequent during weeks in late July, and early August including two weeks in July with recorded PDI values below -4 on eight separate occasions. Winter weeks in December and January also experienced a high frequency of droughts. Very wet to extreme wetness weeks were most numerous in April-May, and August- September with maximum frequency of seven separate times. The total frequency of drought and wet weeks in the East Central division was nearly equal (294 vs 271). Improvement weeks where the Z index increased from a negative to positive value effectively ending a drought are illustrated in Fig. 34 and 35. AWDN precipitation increased at the southern stations and decreased slightly at the northern stations during a small Z index transition of 0.66 (Fig. 34). AWDN precipitation increased dramatically at most stations (up to 3.58 ) causing a large Z index improvement of 3.72 (Fig. 35). 57

72 Figure 31. As in Figure 11, but for Nebraska s East Central climate division. 58

73 Figure 32. As in Figure 12, but for Nebraska s East Central climate division. Figure 33. As in Figure 13, but for Nebraska s East Central climate division. 59

74 Figure 34. As in Figure 14, but for Nebraska s East Central climate division. Figure 35. As in Figure 15, but for Nebraska s East Central climate division. 60

75 4.6 Southwest Climate Division The Southwest climate division experienced variable precipitation and soil moisture conditions throughout the period of record Based on precipitation, dry years included 2000, , 2006 and ; wet years included 1999, 2001, , and The East Central division was in a drought period (PDI<-1) 37% of the time and in a wet spell (PDI>1) 42% of the time. The average weekly AWDN soil moisture illustrated in Fig. 36 ranged from 0.06% to 31%. Soil moisture recharge was most noticeable after major precipitation events. The greatest increases in soil moisture occurred in the spring and summer weeks of 2003, 2007, and 2011 (Fig. 36). The frequency of droughts and wet periods are illustrated in Fig. 37 and 38. Severe to extreme droughts were most frequent during summer weeks of June-August including three weeks in late June with recorded PDI values below -4 on nine separate occasions. Weeks of very wet to extreme wetness were most prominent in spring and winter with the maximum frequency occurring from late November-early February. There was an overall higher frequency of PDI weeks in the wet category than dry category in the Southwest division. Improvement weeks where the Z index increased from a negative to positive value effectively ending a drought are illustrated in Fig. 39 and 40. AWDN precipitation increased at all but one station during a small Z index transition of 0.44 (Fig. 39). AWDN precipitation increased at all stations especially the western stations promoting a large Z index improvement of 2.75 (Fig. 40). 61

76 Figure 36. As in Figure 11, but for Nebraska s Southwest climate division. 62

77 Figure 37. As in Figure 12, but for Nebraska s Southwest climate division. Figure 38. As in Figure 13, but for Nebraska s Southwest climate division. 63

78 Figure 39. As in Figure 14, but for Nebraska s Southwest climate division. Figure 40. As in Figure 15, but for Nebraska s Southwest climate division. 64

79 4.7 South Central Climate Division The South Central climate division experienced variable precipitation and soil moisture conditions throughout the period of record According to precipitation, dry years included 2000, , 2009, and ; wet years included 1999, 2001, , and The East Central division was in a drought (PDI<-1) 34% of the time and in a wet spell (PDI>1) 45% of the time throughout the period of record. The average weekly AWDN soil moisture depicted in Fig. 41 was mainly high (above 20%) at all layers throughout the period of record. Soil moisture recharge was most noticeable after major precipitation events. The greatest increases in soil moisture occurred in the spring and summer weeks of 2007, 2008, and 2011 (Fig. 41). The frequency of droughts and wet periods are illustrated in Fig. 42 and 43. Severe to extreme droughts were most frequent during summer weeks from July-September including three weeks with recorded PDI values below -4 on seven separate occasions. Winter weeks in December and January also experienced a high frequency of droughts. Weeks of very wet to extreme wetness were most abundant in winter and spring with the maximum frequency occurring in April. There was an overall higher frequency of PDI weeks in the wet category than dry category in the South Central division. Improvement weeks where the Z index increased from a negative to positive value effectively ending a drought are illustrated in Fig. 44 and 45. AWDN precipitation increased between 1.27 and 1.47 at all stations during a small Z index transition of 0.51 (Fig. 44). AWDN precipitation increased between 1.67 and 2.20 at all stations during a large Z index improvement of 3.45 (Fig. 45). 65

80 Figure 41. As in Figure 11, but for Nebraska s South Central climate division. 66

81 Figure 42. As in Figure 12, but for Nebraska s South Central climate division. Figure 43. As in Figure 13, but for Nebraska s South Central climate division. 67

82 Figure 44. As in Figure 14, but for Nebraska s South Central climate division. Figure 45. As in Figure 15, but for Nebraska s South Central climate division. 68

83 4.8 Southeast Climate Division The Southeast climate division experienced variable precipitation and soil moisture conditions throughout the period of record Based on precipitation, dry years included 2000, , 2006, 2009, and ; wet years included 1999, 2001, 2005, and and The East Central division was in a drought (PDI<- 1) 38% of the time and in a wet spell (PDI>1) 25% of the time throughout the period of record. The average weekly AWDN soil moisture depicted in Fig. 46 was mainly high (above 20%) at all layers throughout the period of record. Soil moisture recharge was most noticeable after major precipitation events. The greatest increases in soil moisture occurred in the spring and summer weeks of 2003, 2007, 2012, and 2013 (Fig. 46). The frequency of droughts and wet periods are illustrated in Fig. 47 and 48. Severe to extreme droughts were most frequent during summer, fall, and winter weeks from July- December including five weeks with recorded PDI values below -3 on seven separate occasions. Very wet weeks were most abundant in spring with the maximum frequency occurring in March and May. There was an overall higher frequency of PDI weeks in the dry category than wet category in the Southeast division. Improvement weeks where the Z index increased from a negative to positive value effectively ending a drought are illustrated in Fig. 49 and 50. AWDN precipitation increased most at the eastern stations and decreased by 0.05 at the southwest station during a small Z index transition of 0.53 (Fig. 49). AWDN precipitation increased by over 3.00 at two stations during a large Z index improvement of 3.04 (Fig. 50). 69

84 Figure 46. As in Figure 11, but for Nebraska s Southeast climate division. 70

85 Figure 47. As in Figure 12, but for Nebraska s Southeast climate division. Figure 48. As in Figure 13, but for Nebraska s Southeast climate division. 71

86 Figure 49. As in Figure 14, but for Nebraska s Southeast climate division. Figure 50. As in Figure 15, but for Nebraska s Southeast climate division. 72