Visualizing Drought
The impacts of drought depend on time-scale. On short time-scales, drought means dry soil. On long time-scales, it means dry rivers and empty reservoirs. A region may simultaneously experience dry conditions on one time-scale and wet conditions on another e.g. wet soil but low streamflow or visa versa.
Standardized Precipitation Index (SPI) is a widely used measure of drought which can be defined for any time-scale of interest. For any location, SPI is normally distributed with zero mean and unit standard deviation. Index values > 2 indicate exceptionally wet conditions for that location, values < -2 indicate exceptionally dry conditions for that location, etc. Historical precipitation is the only input needed to compute SPI.
Australia experienced drought between 2002 and 2007. The image below shows SPI computed for a location in the drought-prone Murray-Darling basin of New South Wales. The time-series run from Jan 1948 to Jan 2010 and the index was calculated for time-scales from 1 to 12 months. Precipitation data is from NCEP Reanalysis [1] in a 1.875° × 1.875° grid cell centred at 30°S 145°E.
The drought of 2002 to 2007 shows up very clearly. It was preceeded by a wet period between 2005 and 2001. While 2009 showed an episode of severe drought at short time-scales, SPI at was normal/wet at longer time-scales during 2009. Agricultural yields recovered.
Calculating SPI-M
Empirical rainfall probability distributions are far from normal (gaussian) and often approximate a shifted gamma distribution. The empirical cumulative probability distributions are used to transform the rainfall time-series into time-series of percentile probabilities. A normally distributed precipitation index is found by pretending that these percentile probabilities derive from a standard cumulative normal distribution and inverting to find the index values.
This is simple in R. If the vector data contains rainfall infall data, then:
fit.cdf <- ecdf(data)
cdfs <- sapply(data,fit.cdf)
SPI <- qnorm(cdfs)
Tha rainfall data are M-month moving averages (current and previous months). A separate index is calculated for each calendar month to remove seasonality. The R code used to compute SPI values (based in NCEP Reanalysis or other data sets such as GCPC) is here.
[1] The NCEP/NCAR 40-year reanalysis project, Bull. Amer. Meteor. Soc., 77, 437-470, 1996
March 6, 2010
Tags: R, time-series, water stress Posted in: Uncategorized 
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Ensemble Prediction
Weather is unpredictable. Small differences in initial conditions can develop into big differences in the pattern of circulation, in the timing and location of cyclones, rainfall etc. This is true no matter how good the initial observing system is.
The approach taken by organisations such as ECMWF or NCEP is to re-run numerical forecast models with a range of carefully chosen initial conditions. The collection of runs is called the ensemble. Ensemble prediction systems (EPS) give probabilistic forecasts for variables such as rainfall, temperature etc. Current operational EPS have 20 (GFS)Â or 51 (ECMWF) ensemble members from which the probability distributions are derived. ECMWF give an overview of their system here. The probability distributions capture part of the intrinsic uncertainty in weather or climate.
The graph below shows histograms of 20 ensemble member temperatures near some major cities. The data were extracted from NCEP GENS 16-day 2m temperature forecast produced at 00UTC 2 Feb 2010 (i.e GFS forecasts for 18 Feb).
The maps below show some corresponding ensemble statistics for the entire globe (1° resolution, equal area cylindrical projection).
The upper map indicates that forecast uncertainty (standard error) is high between 40° and 60° in both hemispheres (related to the chaotic behaviour of jet streams.) Currently, 16 day temperatures north of Lake Baikal in Siberia are very uncertain, for example. The contours indicate ensemble median temperatures.
Skewness in ensemble temperatures is shown in the lower map. For example, large negative skewness is found in north central US, eastern mediterranean, and Paraguay/Mato Grosso. This suggests tail risk of low temperatures relative to ensemble mean in these areas.
EPS is the future of weather and climate forecasting. These systems produce huge amounts of data. Building useful applications of EPS is both a challenge and an opportunity.
For anyone interested, the R code used to produce these graphs is given here.
February 2, 2010
Tags: R, weather forecast Posted in: Uncategorized No Comments
