DROUGHT FORECASTING
AASC2016 Santa Fe, 20160701
Gregg Suhler
Dynamic Predictables
Slide 2. The Primitive Equations
v
1
r 1
 v  v   p  g    v     v  .............. 1

t

r 
 
  

 T

cV    v T   p  v   q......................................................  2 
 t


 v     v  0....................................................................  3
t
p   RT ...........................................................................................  4 
Slide 3. Oscilliatory Approach
1
1
sin  p t    cos v t     sin  p   v t       sin  p   v t     ......(5)
2
2
  R  R 6cos( 6t )+R12cos(12t )
12   p  v .......................................(6a)
6   p  v ........................................(6b)
p 
12   6 
........................................(7a)
2
   
 v  6 12 .........................................(7b)
2
Slide 4.Sum & Difference Cascade
ULTRASUBHARMONIC SEQUENCE
(FOR 12/6 MONTH FORCING)
7
6
64
5
GENERATION
32
4
16
3
8
2
4
1
2
0
-2
-1
0
1
2
3
4
LOG(BASE 2) PERIOD (YEARS)
5
6
7
Slide 5. System Response by
generation N w 12,6 m forcing.
N=INPUT
GEN
T1 (GT
T2)
T2
W1=1/T1
W2=1/T2
(W1+W2)/
2 = w1
(W2W1)/2 =
w2
t1+ SUM
t2-DIF
2^N/t1+
2^N/t2-
1
1
0.5
1
2
1.5
0.5
0.666667
2
3
1
2
1
0.666667
1
1.5
1.25
0.25
0.8
4
5
1
2
2
1
0.5
1
0.75
0.25
1.333333
4
3
1
2
0.666667
0.5
1.5
2
1.75
0.25
0.571429
4
7
1
2
2
0.5
0.5
2
1.25
0.75
0.8
1.333333
5
3
#6. Oregon01 Coastal precip
#7. Sherwood3N ND. precipitation
#8. Colorado04 (Platte) Precip201001-
#9.CA06pcp Pred 201001-
Slide #10 AASC2016SantaFe 20160701. “As Above, So Below” Thoth, Egyptian God of Science
GRL, VOL 26, NO.6, PAGES 763-766, MARCH 15, 1999
Unified Structure in Quaternary Climate, by John H Gauthier (at Sandia NL in 2015)
ABSTRACT. The Quaternary climate record exhibits a structure of superimposed, aperiodic oscillations starting at the 11-yr
sunspot cycle and spaced by powers of 2 in period through the major 90,000-yr glacial cycle. Climate cycles that do not fall
in this structure typically correspond to harmonics of the structure oscillations. The inclusion of the known solar cycles and
the presence of increased abundances of cosmogenic radionuclides at many structure periods suggest that the structure is
related to long-period solar variability.
The Climate Record. Climatologist have recently noted that some climate oscillations occur at fractions—1/2, 1/4, 1/8, and
1/16—of the period of the 23-ky (ky=1000yr) Milankovitch precessional cycle [Kerr, 1996]. Curiously when extrapolated
downward, this sequence includes the periods of the known solar cycles: 1/256 coincides with the 88-yr Gleissburg solar
cycle; 1/1024 is the 22-yr solar magnetic cycle; 1/2048 is the 11-yr sunspot cycle. Re-examination of data from numerous
climate proxies (materials that carry the imprint of past climate) indicates that this relationship is pervasive. Swings in climate
over time scales from the 11-yr sunspot cycle to the 90-ky glacial cycle tend to a unified geometric structure of superimposed,
aperiodic oscillations spaced by powers of 2 in period.
Journal of Climate, 15 March 2001, pp 1323-28. Qi Hu and Song Feng, A Southward Migration of Centennial-Scale Variations
of Drought/Flood in Eastern China and the Western United States.
ABSTRACT. Several studies of the established warm season climate records for eastern China (1470-1997) showed
alternating dry and wet periods at centennial scales. The spatial patterns show that when a dry condition or drought was
observed in southern China, a wet or flood situation was found in the northern part of eastern China and vice versa. These
patterns suggest a meridional variation of the centennial-scale wet/dry anomalies.
This study analyzed the same data and showed that the dry and wet anomalies initially appeared in the northern part of
eastern China and then migrated southward to affect the low latitudes. An extension of this analysis to the United States
revealed a similar southward migration of dry/wet anomalies that first developed in the high latitudes in the western part of the
country. The average speed of the migrations in both areas is about 3.0 degrees of latitude per 10 years.
The results suggest that mechanisms in mid- and high latitudes may play critical roles in the development of drought in highas well as subtropical-latitude regions. The findings also indicate key areas to monitor for prediction of extended periods of
frequent droughts or floods in “downstream” regions in the migration of the centennial scale anomalies.
Earlier slides have introduced the role of 2^N (N as +/- integer) as special yet oft obtained case in Forced System Response.
Gauthier’s 1999 paper cites astronomical period forcing and response functions and importantly notes what is observed can be
both forcer and responder in an intricately interactive yet highly ordered system.
Hu and Song in the 2001 paper find two significant regional long periods at 130 and 85 years (near 128 and 256/3 years) as did
Hameed et al (126, 84, 56yr (near 3600/16225/4 yr) in 1983 for Beijing precipitation.
Precipitation prediction examples shown use climate division and coop stations. The focus has been on Drought but, of necessity
shown Flood as appropriate.
Shakespeare: MacBeth Witches Chants
Double, Double, Toil and Trouble: Annotations for the Witches' Chants (4.1.1-47)
A dark cave. In the middle, a boiling cauldron.
Thunder.
Enter the three Witches
First Witch
Thrice the brinded cat hath mew'd.
Second Witch
Thrice and once the hedge-pig whined.
Third Witch
Harpier cries "'Tis time, 'tis time."
First Witch
Round about the cauldron go;
In the poison'd entrails throw.
Toad, that under cold stone
Days and nights has thirty-one
Swelter'd venom sleeping got,
Boil thou first i' the charmed pot.
All
Double, double, toil and trouble; (10)
Fire burn, and cauldron bubble.