Introduc)on to Drought Indices Xiaomao Lin Department of Agronomy Kansas State University xlin@ksu.edu - - WMO Workshop, Pune, India 3 rd - 7 th October 2016 Photo: Tribune, Kansas, March 2013 by X. Lin
Outline of the Talk I. Defini)on of drought II. Drought indices : PDSI, SPI, and SPEI III. Drought data analysis 2
What is drought? Drought is a condi)on of moisture deficit sufficient to have an adverse effect on vegeta)on, animals, and man over a sizeable area. (Warwick, 1975) a) Slow- onset, creeping phenomena b) Rela)ve condi)on of moisture deficit c) Drought impacts spread over large areas 3
What is drought? Meteorological drought: "A period of abnormally dry weather sufficiently prolonged for the lack of water to cause serious hydrologic imbalance in the affected area." (Huschke, R.E., ed., 1959, Glossary of meteorology, American Meteorological Society, 638 p.) Agricultural drought: "A climatic excursion involving a shortage of precipitation sufficient to adversely affect crop production or range production." (Rosenberg, N.J., ed., 1979, University of Nebraska, Lincoln, March 26-28: Littleton, Colorado, Water Resources Publications, 225 p.) Hydrologic drought: "A period of below average water content in streams, reservoirs, groundwater aquifers, lakes and soils." (Yevjevich Vujica, Hall, W.A., and Salas, J.D, eds., 1977, Colorado State University, Fort Collins, Colorado, 276 p.) 4
Palmer Drought Severity Index (PDSI) PDSI Classifica)ons 4.00 Extremely wet 3.00 to 3.99 Very wet Wet 2.00 to 2.99 Moderately wet 1.00 to 1.99 Slightly wet.50 to.99 Incipient wet spell.49 to.- 49 Near normal -.50 to -.99-1.00 to - 1.99-2.00 to - 2.99 Incipient Drought Mild Drought Moderate Drought Dry - 3.00 to - 3.99-4.00 Severe Drought Extreme Drought 5
Calcula)on Procedures of PDSI Note II: Step I: PET (Thornthwaite, 1948) C = 1.6; Ta is mean temperature; d is average day lengths (hours); I = sum ((Ta/5)^1.514 ) on annual basis; N = number of days in the month; a = a funcson of I (3- order polynomial eq.) Note I: If Ta <=0, PET =0; If 0< Ta <= 26.5 o C. If Ta > 26.5 o C.
Step II: Two- layer surface water balance by ET, R, PR, RO, PRO, L, and PL Recharge Runoff Loss Notes: Surface layer (s) ( AWC s ) = 1 (25mm layer); Underlying Layer (u) AWC u = AWC AWC s
Step III: Coefficients for four variables for each month (j = 1 12)
Step IV: Calibra)on of CAFEC (1931-1990 or longer) ( d is moisture departure from normal ) This is the water balance idea too - - - Clima)cally Appropriate for Exis)ng Condi)ons (CAFEC) Calibra)on is much similar to the calcula)ons of climatology over a base period. Calibra)on Base Period: NOAA used: 1931 1983 or 1931 1990
Step V: Formulate an index Z (standardized for various loca)ons and months) Z = d K i Z is the moisture anomaly index K i is a weigh)ng factor (Palmer said) but, its meaning is a ra)o of supply and demand Notes: 1. Both K i and D i bar here are calibrated (calculated) from calibra)on period ONLY. 2. Numerical constants here are tuned ini)ally from KS and IA, then finalized by using KS, IA, PA, OH, ND, TN, and TX (7 states).
Step VI: Beta version of PDSI 13 points from Western Kansas and Central Iowa to set a cap for PDSI = - 4.0 Palmer here defined X = PDSI as following equa)on:.. (PDSI eq.)
Palmer could have stopped here for his study so that the PDSI would perhaps be appropriately termed as a hydrological drought index. However, he wanted to have a meteorological drought index, which requires when dry (wet) spells start and end. Step VII: Percentage Probability Calcula)on U(i)=Z(i)+0.15 In a drought U(i)=Z(i) 0.15 In a wet spell
Step VIII: Assign the X1, X2, and X3 for PDSI Notes (Palmer 1965): When a drought or wet spell has become established and 0 < Pe < 100, a value for the PDSI cannot be assigned un)l Pe reaches 0 or 100. Notes (Weather and Crop Bulle)n when opera)onal mode): X = X3, when 0 < Pe <= 50 X = X2 or X1, when 50 < Pe < 100 and whichever has opposite sign of X3
Summary: PDSI is a func)on of precipita)on, temperature, and soil available water capacity
Standardized Precipita)on Index (SPIxx) Dry Wet - - - McKee et al. 1993 15
Computa)on of SPIxx Step I: Formulate accumulated ( m months ) )me series Step II: Using Maximum Likelihood Es)mate to find the distribu)on s parameters - - - gamma probability density func)on Step III: Standardized R t to obtain index Requirements: >=30yr monthly obs. (precipita)on); xx ()me scale interval) is from 3 to 24 (48) months
Standardized Precipita)on- Evapotranspira)on Index (SPEIxx) - - - The SPEI takes into account both precipita)on and poten)al evapotranspira)on (PET) in determining drought. SPEI Dry Wet --- Vincente- Serrano et al., 2010 17
Computa)on of SPEIxx Step I: Calculate monthly PET (Thornthwaite method) Step II: Calculate difference series (d i ) d i = P i PET i Step III: Formulate accumulated ( m months ) d i )me series A i = d i + d i 1 +... + d i m+1 Step IV: Find the distribu)on s parameters - - - three- parameter log- logis)c probability distribu)on (shape (alpha), scale (beta), and origin (gamma))
Drought data analysis RelaSve Frequency DuraSon Severity Intensity Return Period 19
Example: Empirical cumula)ve frequency East Central West PDSI drought frequency higher than SPEI for all regions Western Kansas has the highest PDSI drought frequency by up to 10% Eastern Kansas is only 3-5% higher - - - Zambreski s Thesis, 2016 20
Comparison between SPIxx and SPEIxx Subtle differences between SPI/SPEI intensity Most intense SPEI- 6 drought in 2012 SPEI- 12/24 intensises rivaled 1950s /1930s shorter durason - - - Zambreski s Thesis, 2016 21
Example: A close- up look at western Kansas 22
Example: Drought during crop growing seasons 23
Example of PET Sensi)vity at one Sta)on in Kansas (1895 to 2012) 24
Examples of Return Severity - - - Zambreski s Thesis, 2016 25
Examples of Drought Analysis in the USA 26
Summary Drought is a disaster/ natural phenomenon. Drought is a normal part of the diverse climate (drought aridity). SPI (precipita)on); SPEI (precipita)on & PET); and PDSI (precipita)on, temperature (PET), and soil water balance models). Monitoring and early warning system are cri)cal. Beuer synthesis/analysis of climate data could help trigger set ac)ons within a drought plan. The water- limited environments account of half of earth s land surface and are projected to con)nue to expand. Drought will likely play an increasing role in the future as demand increases from finite water resources. Climate change scenarios could be a base for us to make appropriate drought planning decisions. 27
Acknowledgments: Director, Mike Hayes, National Drought Mitigation Center (NDMC), University of Nebraska 28
Drought impacts 29
Examples of drought impacts: intensity, dura)on, areal extent, and economic loss 2012 Drought Impacts " Economic loss estimates " $30 billion, NCDC " Crop indemnities: $17 billion " 2011 the previous record with $10.8 billion --- from NOAA, NDCD, and National Drought Mitigation Center 30
Examples of summer droughts PDSI: 1934 Summer (JJA) PDSI: 2011 Summer (JJA) 31