A A Palmer Drought Severity Index Palmer Drought Severity Index for the NARR and ERA-40: for the NARR and ERA-40: Linkages to Large-Scale Circulation and Climate VariabilityLinkages to Large-Scale Circulation and Climate Variability

S. Nigam, A. Ruiz-Barradas S. Nigam, A. Ruiz-Barradas andand A. Dai A. Dai

K. KarnauskasK. Karnauskasand thanks to…and thanks to…

OutlineOutline

1.1. Lightning review of drought and PDSILightning review of drought and PDSI

2.2. Algorithm implementation and new developmentsAlgorithm implementation and new developments(read: my life for the past few months… over 1,700 lines of code later)(read: my life for the past few months… over 1,700 lines of code later)

3. Results3. Resultsa. Spatial patternsa. Spatial patternsb. Interannual variabilityb. Interannual variability

4. Linkages with general circulation, climate variability4. Linkages with general circulation, climate variability

Basic Drought ReviewBasic Drought Review

• A deficiency in precipitation, with respect to the climatologically appropriate soil moisture conditions.

• Can be short term or long term. Recall that there can be short term moist spells in the midst of a long term drought.

• Short-term often related to an anomalous weather event, and long term often related to anomalies in large-scale circulation.

• Different regions respond to precipitation in different ways. 2” below normal monthly rainfall in one region could mean substantial drought, whereas other regions might be able to withstand 10” below normal.

Basic PDSI ReviewBasic PDSI Review

• Formulated by Wayne Palmer of the U.S. Weather Bureau in 1965.

• A very complicated index that that tells you the severity of meteorological drought in a location.

• Ranges from –4 (extreme drought) to +4 (extremely moist)

• Most widely used drought index in the US.

• Takes a supply-and-demand approach to the surface water balance.

To summarize the derivation…

Z = K [ P – ( αPE + βPR + γPRO – δPL ) ]

Advantages of the PDSIAdvantages of the PDSI

• All that is needed is precipitation, temperature, available water content, and a little information specific to the locale (e.g. about regional climate and soil type). Do not need streamflow.

• PDSI is a good measure of long-term drought; order several months.

• In addition to drought, PDSI provides information about wet spells.

• Standardization to local climate means we can look at a map and compare the conditions in TX with the conditions in MA and we are still comparing apples to apples.

• Built in timescale so good for “real” drought… not fluctuations within a single month.

Disadvantages to PDSIDisadvantages to PDSI• Not good for short-term drought, e.g. weeks.

• Standardization process has little statistical or physical justification (Alley, 1984).

• Not good if your region or “climate division” isn’t very homogeneous.

• Precipitation in one month can have a large effect on the PDSI of previous months (Alley, 1984).

• Computation of the coefficients highly sensitive to base period used (Karl, 1986).

• Not useful in calculating supplies of snow-locked water, so much better east of the continental divide (USGS FAQ).

• Does not utilize potentially useful streamflow information.

• In the surface water balance used, no runoff is allowed until the surface and subsurface layers are full… so underestimates runoff.

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Other Drought IndicesOther Drought IndicesPalmer-Z Just the monthly anomaly of conditions via PDSI. Good for

looking at “now.”

SPI Standardized precipitation index. Tells you the probability of precipitation on any time scale. Good for looking into future.

PHDI Palmer hydrological drought index. Gauges groundwater and reservoirs, for even longer timescales than PDSI itself.

CMI Crop Moisture Index. For short-term drought on order of weeks.

SWSI Surface Water Supply Index. Good for places where snow is abig player in the surface water supply, e.g. Colorado.

• The CPC also has many experimental and blended types of indices.

• Hey, there is always “inches below normal” or “percent below normal.”

Algorithm Development & ImplementationAlgorithm Development & ImplementationGoal of Dai et al. (2004) Develop and implement the PDSI algorithm, using any data

available, to produce the best possible representation ofPDSI over the global domain and back to 1870.

My objective Take the NARR and all that the NARR offers, and developan implementation of the PDSI, minimizing external data, toassess the suitability of the NARR to hydroclimate studiesas they relate to meteorological drought. Same for ERA-40.

NARRTemperaturePrecipitationEvapotranspirationPotential evapotranspirationSurface runoffSubsurface runoff0-2m soil moisture

ERA-40TemperaturePrecipitationEvapotranspirationPotential evapotranspirationSurface RunoffSubsurface runoffSoil layer 1 moistureSoil layer 2 moistureSoil layer 3 moistureSoil layer 4 moisture

ExternalSoil moisture capacity (ORNL)

Development of a pseudo 2Development of a pseudo 2ndnd soil layer for NARR soil layer for NARR

Development of a PE scheme for ERA-40Development of a PE scheme for ERA-40

NARR:Set up variables

Open filesRead in data

Tons of conversions

Set up water balanceSplit up NARR’s soil layerDeal with potential loss,

Recharge, etc.

Calculate someclimatologies, and the

climate coefficients(alpha, beta, etc),and “potential”

ratios

Calculate local climatecoefficients

Determine precipdeficit

Calculate Z andPDSI, write to files

and close up

ERA-40: Implement PE scheme

Z(t) = K(m) * [ P(t) – ( α(m)*PE(t) + β(m)*PR(t) + γ(m)*PRO(t) – δ(m)*PL(t) ) ]PDSI(t) = 0.9 * PDSI(t-1) + 0.3 * Z(t)

T H E C O D ET H E C O D E

NARR ERA-40

Dai

Long Term Mean/Long Term Mean/Annual AverageAnnual Average

PDSIPDSI

NARR ERA-40

Long Term Mean/Long Term Mean/Annual AverageAnnual Average

Palmer-ZPalmer-Z

NARR ERA-40

PDSI 12/1985PDSI 12/1985

DaiNOAA

NARR ERA-40

Dai

PDSI 7/1992PDSI 7/1992

NOAA

NARR ERA-40

Palmer-Z 3/1987Palmer-Z 3/1987

NOAA

(no Dai Palmer-Z)

PDSI June 1988

Dai

NARR ERA-40

NOAA

NARR ERA-40

NOAA

(no Dai Palmer-Z)

Palmer-Z June 1988

PDSI / Interannual VariabilityPDSI / Interannual Variability

Dai

NARR ERA-40

STANDARD DEVIATION

Sigma-based indices:35°N – 47°N x 105°W – 95°W

PDSI / Interannual VariabilityPDSI / Interannual Variability

STANDARD DEVIATION

Sigma-based indices:35°N – 47°N x 105°W – 95°W

NARR ERA-40Dai

LOW PASS FILTERED 0.083 mo-1 LOW PASS FILTERED 0.083 mo-1

R=0.55 (99.9%) R=-0.50 (99.9%)

R=0.64 (99.5%)

NORMALIZED

Autocorrelations

Power spectra

NARR ERA-40DaiR=0.55 (99.9%) R=-0.50 (99.9%)

NORMALIZED

PDSI Variability / 1PDSI Variability / 1stst EOF EOF

Dai23.3%

NARR21.3%

ERA-4026.3%

1st Principle Component intercorrelations:

Dai vs. NARR ~0Dai vs. ERA-40 0.34 *NARR vs. ERA-40 0.65 *

Scaled by RMS of PC

* Significant at the 99.9% confidence level.

Remember the sign ofeigenvector is arbitrary

PDSI Variability / 2PDSI Variability / 2ndnd EOF EOF

Dai17.1%

NARR17.1%

ERA-4020.2%

Scaled by RMS of PC

2nd Principle Component intercorrelations:

Dai vs. NARR -0.12Dai vs. ERA-40 -0.26 *NARR vs. ERA-40 0.61 ** Significant at the 99.9% confidence level.

Remember the sign ofeigenvector is arbitrary

PDSI Variability / 3PDSI Variability / 3rdrd EOF EOF

Dai7.8%

NARR9.1%

ERA-409.6%

Scaled by RMS of PC

3rd Principle Component intercorrelations:

Dai vs. NARR 0.39 *Dai vs. ERA-40 ~0NARR vs. ERA-40 0.49 ** Significant at the 99.9% confidence level.

Remember the sign ofeigenvector is arbitrary

Palmer-Z Variability / EOFsPalmer-Z Variability / EOFsNARR 1st EOF (25.3%)

ERA-40 1st EOF (33.8%)

NARR 2nd EOF (9.7%)

ERA-40 2nd EOF (9.4%)

NARR 3rd EOF (7.6%)

ERA-40 3rd EOF (8.3%)

Scaled by RMS of PCRemember the sign ofeigenvector is arbitrary

PDSI / General Circulation LinkagesPDSI / General Circulation LinkagesPacific Decadal Variability (PDO)…

Dai PC2 vs. PDO -0.25 *

NARR PC2 vs. PDO -0.24 *

* Significant at the 99.9% confidence level.

……after 1987after 1987 -0.49 *-0.49 *

Courtesy JISAOU. Washington

PDSI / General Circulation LinkagesPDSI / General Circulation Linkages

Arctic Oscillation (AO)…

NARR PDSI Index vs. AO 0.14 *NARR PC1 vs. AO 0.12 *NARR EOF1 similar to AO? (click)

ERA-40 PDSI Index vs. AO 0.28 **ERA-40 PC1 vs. AO 0.11

Very small correlations with ENSO, PNA

* Significant at the 95% confidence level.** Significant at the 99.9% confidence level.

Courtesy JISAOU. Washington

Courtesy JISAO,U. Washington

NARR 1st EOF (25.3%)

?

ReferencesReferencesAlley, W. M. 1984. The Palmer Drought Severity Index: Limitations and assumptions. J. Climate and Appl. Meteor. 23:1100–1109.

Barlow, M., S. Nigam, and E. H. Berbery, 2001: ENSO, Pacific decadal variability, and U.S. summertime precipitation, drought, and streamflow. J. Climate, 14, 2105-2128.

Black, T.L., 1994: The new NMC mesoscale eta model: Description and forecast samples. Weather Forecasting, 9, 265-278.

Dai, A., Trenberth, K. E. and T. Qian, 2004: A Global Dataset of Palmer Drought Severity Index for 1870-2002: Relationship with Soil Moisture and Effects of Surface Warming. J. Hydrometeor., 5, 1117-1130.

European Centre for Medium-Range Weather Forecasts, 2002: The ERA-40 Archive. Reading, ECMWF, 40 pp.

Heim, Jr., R. R., 2002: A review of Twentieth-Century drought indices used in the United States. Bull. Amer. Meteor. Soc., 83, 1149-1165.

Kalnay, E. and Coauthors, 1996: The NCEP/NCAR Reanalysis 40-year Project. Bull. Amer. Meteor. Soc., 77, 437-471.

Karl, T. R., 1986: The sensitivity of the Palmer Drought Severity Index and Palmer's Z-Index to their calibration coefficients including potential evapotranspiration. J. Climate Appl. Meteor., 25, 77-86.

Messinger, F. G., and Coauthors, 2004: NCEP North American Regional Reanalysis. Paper P1.1, 15 th Symp. on Global Change and Climate Var., Comb. Preprints CD-ROM, Amer. Meteor. Soc., Seattle, WA, 11-15 January.

Nigam, S., M. Barlow, and E. H. Berbery, 1999: Analysis links Pacific decadal variability to drought and streamflow in United States. EOS 80: 621, 622, 625.

Palmer, W. C, 1965: Meteorological Drought. Res. Paper No.45, 58pp., Dept. of Commerce, Washington, D.C.

Riebsame, W. E., S. A. Changnon, and T. R. Karl, 1991: Drought and natural sesources management in the United States: impacts and implications of the 1987-89 drought. Westview Press 11-92.

Schubert, S., Suarez, M., Pegion, P., Koster, R., J. Bachmeister, 2004: Causes of Long Term Drought in the U.S. Great Plains. J. Clim. 17, 485.

Tianwen, C. and C. Weixin, 1980: Measurement and estimation of field evaporation and potential evaporation, Collected Geographical Papers, Science Press, Beijing.

Wells, N., Goddard, S., and M. J. Hayes, 2004: A Self-Calibrating Palmer Drought Severity Index. J. Climate, 17(12), 2335-2351.