A Copula-Based Multi-Index Approach
for Global Drought Monitoring and
Prediction
Amir AghaKouchak
Department of Civil and Environmental Engineering
University of California, Irvine
Drought Definition and Indicators
Different drought indices
Precipitation, soil moisture):
based
on
different
climate
variables
(e.g.,
• Standardized Precipitation Index (SPI)
• Standardized Soil Moisture Index (SSI)
• Standardized runoff Index (SRI)
• Palmer Drought Severity Index (PDSI)
Precipitation (D-Scale) – Jan 2012
Soil Moisture (D-Scale) – Jan 2012
GIDMaPS: Global Integrated Drought Monitoring and Prediction System
http://drought.eng.uci.edu/
GIDMaPS: Global Integrated Drought Monitoring and Prediction System
http://drought.eng.uci.edu/
Meteorological Drought
Agricultural Drought
GIDMaPS: Global Integrated Drought Monitoring and Prediction System
http://drought.eng.uci.edu/
Meteorological Drought
Agricultural Drought
Meteo-Agricul. Drought
GIDMaPS: Global Integrated Drought Monitoring and Prediction System
Multi-Index Drought Monitoring
Multi-Index Drought Monitoring
3-, 6- and 12-month drought conditions based on Standardized
Precipitation Index (SPI) and Standardized Soil Moisture Index (SSI) for
Climate Division 3 in California.
Multi-Index Drought Monitoring
A Multi-Index Approach Using a Joint Distribution Function
P ( X  x, Y  y )
p  C F ( X ), G (Y )
C is the copula and F(X) and G(Y) are the marginal cumulative distribution
functions of precipitation (X) and soil moisture (Y), respectively
Multivariate Standardized Drought Index (MSDI)
MSDI  
1
 p
where ɸ is the standard normal distribution function.
Hao Z., AghaKouchak A., 2013, A Nonparametric Multivariate Multi-Index Drought
Monitoring Framework, Journal of Hydrometeorology, 15, 89-101.
Hao Z., AghaKouchak A., 2013, Multivariate Standardized Drought Index: A Parametric
Multi-Index Model, Advances in Water Resources, 57, 12-18.
Multi-Index Drought Monitoring
Standardized Precipitation Index (SPI)
pSPI  P ( X  x )
SPI   1  pSPI 
Standardized Soil moisture Index (SSI)
pSSI  P (Y  y ) SSI   1  pSSI 
Multivariate Standardized Drought Index
(MSDI)
pMSDI  P ( X  x, Y  y )
MSDI   1  pMSDI 
Where: X: accumulated precipitation;
Y: accumulated soil moisture;
φ: standard normal distribution
MSDI (Hao and AghaKouchak, 2013):
• Standardized index similar to SPI
• Improves drought onset detection
• A multi-Index for composite meteorological -agricultural drought monitoring
Multi-Index Drought Monitoring
Standardized Precipitation Index (SPI)
pSPI  P ( X  x )
SPI   1  pSPI 
Standardized Soil moisture Index (SSI)
pSSI  P (Y  y ) SSI   1  pSSI 
Multivariate Standardized Drought Index
(MSDI)
pMSDI  P ( X  x, Y  y )
MSDI   1  pMSDI 
Where: X: accumulated precipitation;
Y: accumulated soil moisture;
φ: standard normal distribution
MSDI (Hao and AghaKouchak, 2013):
• Standardized index similar to SPI
• Improves drought onset detection
• A multi-Index for composite meteorological -agricultural drought monitoring
Multi-Index Drought Monitoring
Standardized Precipitation Index (SPI)
pSPI  P ( X  x )
SPI   1  pSPI 
Standardized Soil moisture Index (SSI)
pSSI  P (Y  y ) SSI   1  pSSI 
Multivariate Standardized Drought Index
(MSDI)
pMSDI  P ( X  x, Y  y )
MSDI   1  pMSDI 
Where: X: accumulated precipitation;
Y: accumulated soil moisture;
φ: standard normal distribution
MSDI (Hao and AghaKouchak, 2013):
• Standardized index similar to SPI
• Improves drought onset detection
• A multi-Index for composite meteorological -agricultural drought monitoring
Multi-Index Drought Monitoring
Standardized Precipitation Index (SPI)
pSPI  P ( X  x )
SPI   1  pSPI 
Standardized Soil moisture Index (SSI)
pSSI  P (Y  y ) SSI   1  pSSI 
Multivariate Standardized Drought Index
(MSDI)
pMSDI  P ( X  x, Y  y )
MSDI   1  pMSDI 
Where: X: accumulated precipitation;
Y: accumulated soil moisture;
φ: standard normal distribution
MSDI (Hao and AghaKouchak, 2013):
• Standardized index similar to SPI
• Improves drought onset detection
• A multi-Index for composite meteorological -agricultural drought monitoring
Multi-Index Drought Monitoring
Standardized Precipitation Index (SPI)
pSPI  P ( X  x )
SPI   1  pSPI 
Standardized Soil moisture Index (SSI)
pSSI  P (Y  y ) SSI   1  pSSI 
Multivariate Standardized Drought Index
(MSDI)
pMSDI  P ( X  x, Y  y )
MSDI   1  pMSDI 
Where: X: accumulated precipitation;
Y: accumulated soil moisture;
φ: standard normal distribution
MSDI (Hao and AghaKouchak, 2013):
• Standardized index similar to SPI
• Improves drought onset detection
• A multi-Index for composite meteorological -agricultural drought monitoring
Multi-Index Drought Monitoring
Sample time series of the 6-month SPI, SSI and MSDI for a grid cell in Texas (Location:
longitude 100 W and latitude 30 N).
Multi-Index Drought Monitoring
Multi-Index Drought Monitoring
1-Month SPI and SSI Derived
Using
NASA
MERRA-LAND
Precipitation and soil moisture
Data.
Multi-Index Drought Monitoring
1-Month SPI and SSI Derived
Using
NASA
MERRA-LAND
Precipitation and soil moisture
Data.
Multi-Index Drought Monitoring
Multi-Index Drought Monitoring
GIDMaPS
D4 D3
D2 D1
D0 W0 W1 W2 W3 W4
GIDMaPS: Global Integrated Drought Monitoring and Prediction System
http://drought.eng.uci.edu/
GIDMaPS: Global Integrated Drought Monitoring and Prediction System
•
•
•
•
Empirical PDF Matching
Mean-Fields Bias Removal
Bayesian-Based Correction Algorithm
Parametric Fitting Correction
Real-Time Data
Global Precipitation Climatology Project + ~18 Months Real-Time Data
~ 32 Years Satellite-Based Rainfall Data
where G and S denote GPCP
and real-time satellite data
(here, PERSIANN and TRMMRT). The conditional probability
P(G|S) indicates the likelihood
of the measurement G given
the satellite observation S.
1950
1979
1998
Present
AghaKouchak A., and Nakhjiri N., 2012, A Near Real-Time Satellite-Based Global Drought Climate Data
Record, Environmental Research Letters, 7(4), 044037, doi:10.1088/1748-9326/7/4/044037.
GIDMaPS: Global Integrated Drought Monitoring and Prediction System
MSDIP-S = C (Precipitation, Soil Moisture)
MSDIp-r = C (Precipitation, Runoff)
Can MSDI be extended to a high dimensional drought indicator
involving all key variables for drought monitoring?
MSDI=C(Precip., Soil Moisture, Runoff, ET, TWS, Temp., …)
What are the opportunities to
move toward a comprehensive
multi-index drought indicator?
GIDMaPS: Global Integrated Drought Monitoring and Prediction System
MSDI=C(Precip., Soil Moisture, Runoff, ET, TWS, Temp., …)
MSDI=C1(C2(Precip., Soil Moisture), Runoff)
MSDI=C1(C2(Precip., Soil Moisture), C3(Runoff, TWS))
What are the opportunities to move toward a comprehensive multi-index drought
indicator? Thought? Feedback? Potential collaborators?
GIDMaPS: Global Integrated Drought Monitoring and Prediction System

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