Products expressed in terms of climate anomalies

1
Products expressed in terms of climate anomalies

• Yuejian Zhu and Zoltan Toth
• Environmental Modeling Center
• NCEP/NWS/NOAA
• November 1st 2005

2
Input climate/forecast data -- current available

• NCEP/NCAR reanalysis data
• 4 cycles (00UTC, 06UTC, 12UTC and 18UTC) per day
• 40 years (Jan. 1st 1959 Dec. 31th 1998)
• Need to consider the systematic difference
  between NCEP/NCAR reanalysis and current analysis
  (GDAS)
• Resolution and format
• 2.52.5 (lat/lon) grid, GRIB-1 format
• 1.01.0 (lat/lon) grid, GRIB-1 format (forecast
  only)
• Variables at levels (possible to add more)
• Height 1000hPa, 700hPa, 500hPa, 250hPa
• Temperature 2m, 850hPa, 500hPa, 250hPa
• Wind 10m, 850hPa, 500hPa, 250hPa
• PRMSL, max/min temperature

3
Climatological mean (estimation)

• To use Fourier expansion from 40 years data and
  compare following four considerations
• Considering first Fourier mode a1 and b1
• Fits to daily data to obtain annual cycle
• Considering first two Fourier modes a1,b1,a2 and
  b2
• Fits to daily data to obtain annual and
  semi-annual cycle
• Considering first three Fourier modes
  a1,b1,a2,b2,a3 and b3
• Fits to daily data to obtain annual, semi-annual
  and 4-month cycle
• Considering first four Fourier modes
  a1,b1,a2,b2,a3,b3,a4 and b4
• Fits to daily data to obtain annual, semi-annual,
  4-month and seasonal cycle

4
Higher moments (estimation)- work on the
anomalies from mean

• Standard deviations
• Based on 4 different daily means (previous slide)
• To get 40 years average daily standard deviation
  first
• To calculate monthly mean of standard deviation
  from daily
• To generate a slope from month to month
• To project to daily standard deviation from month
  mean

5
Products (plan)

• Based on 4 different considerations (choose one)
• Assuming the normal distributions of the 40 years
  climate data
• PDF will be presented by first two moments (mean
  and standard deviation)
• Considering the systematic differences between
  NCEP/NCAR reanalysis and current GDAS
• Using bias corrected forecasts
• To calculate climate anomaly
• For 1x1 degree grid point globally.
• For all 19 variables (height, temperature, wind
  and etc.)
• For each ensemble member.
• Output in percentile (0-100, 50normal).

6
Discussion

• How many modes we need to consider?
• In general, more modes will be better
• First two modes are enough for the heights
• Surface variables and winds are challenged
• Are all variables normal distribution?
• Depends on variables and geographical locations
  (?)
• Most of them are normal distribution
• Examples of 2-meter temperature and 10-meter u
• Monthly distribution of 500hPa height has a
  little seasonal tilt
• Examples of time series for daily mean and
  standard deviation for all 19 selected variables
• Two physical locations (near Washington DC and
  Ottawa)
• Are these plots enough to demonstrate?
• http//wwwt.emc.ncep.noaa.gov/gmb/yzhu/html/CLIMAT
  E_ANOMALY.html

7
Notes for presentation and posted maps

• Next few slides are from early studies
• Based on monthly average of climatology
• Using L-moment and several fitting methods
• Probabilistic extreme forecasts are for future
  NDGD purpose
• Examples of future application for NAEFS
• Visit http//wwwt.emc.ncep.noaa.gov/gmb/yzhu/html/
  CLIMATE_ANOMALY.html
• For four different modes consideration (need
  choose one only)
• January 15th and July 15th are posted to contrast
  of seasonal difference
• 0000UTC and 1200UTC are posted to contrast of
  daily cycle
• November 1st 0000UTC 2005 raw forecasts are used
  as example
• Only one ensemble member is demonstrated
• Differences (reanalysis and GDAS) are not
  considered (not available yet)
• Bias corrected forecasts will be used when final
  application
• Anomaly forecast maps are shown normal (0),
  above normal () and below normal (-)
  respectively
• Maximum and minimum temperatures
• Not quite right! 6 hours climate .vs 12 hours
  forecast (only available right now)
• 6 hours tmax and tmin will be generated soon for
  ensemble system.

8
Climatological mean and higher moments-Early
study

• To consider monthly mean (tested)
• Monthly mean (large data samples 1240)
• Interpolate to daily (shifted from season)
• To consider daily mean (tested)
• 5-day running mean for daily climatology
• Data samples 200
• 5-day center weighted mean for monthly
  climatology
• Data samples 200
• (d-2)0.12(d-1)0.22d0.32(d1)0.22(d2)0.12
  
• Fitting distributions (three parameters)
• Gamma, Pearson type-III, GE3 (generalized
  extreme-value)

9
GEV
Monthly mean 5-day weighted mean
10
GEV
Monthly mean 5-day weighted mean
11
GEV
PE3
PE3
Monthly mean 5-day weighted mean
12
ENSEMBLE 10-, 50- (MEDIAN) 90-PERCENTILE
FORECAST VALUES (BLACK CONTOURS) AND
CORRESPONDING CLIMATE PERCENTILES (SHADES OF
COLOR)
Example of probabilistic forecast in terms of
climatology