Posts Tagged ‘weather forecast’

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)  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.

Visualizing the jet stream

Jet streams are narrow tubes of strong westerly winds which circle the earth at ≈ 10km elevation. These strong winds separate regions of cold and warm air. Surface weather at mid-latitudes is affected by the chaotic meanderings of jet streams.


The above wind speed maps are based on NCEP GFS analysis at 300mb pressure level (equivalent to ≈ 10km). The speed scale is in m/s.

There are many interesting things to notice about these maps. Firstly, there are several (5 or 6) planetary scale meanders of the jet stream. The meanders are called planetary or Rossby waves. Secondly, the enclosed area is larger and wind speeds higher in the northern hemisphere. This situation is reversed during the southern winter. Notice the closed loop of clockwise circulating air close to New Zealand. In this case a jet stream meander has grown large, become unstable and broken off. The loop encloses a pocket of cold air. Such detached loops can persist and remain in the same location for days.

The graphic below shows the GFS 300mb analysis wind speeds for ooUTC 19 Jan 2010 and the forecast wind speeds for 00UTC 20 & 21 January.  Rossby wave propogation can be seen clearly (the ridges and troughs advance anticlockwise in the Northern hemisphere, clockwise in the Southern Hemisphere)



300mb wind velocities (zonal wind component Uvel and meridonal wind component Vvel) at 300mb were extracted from 0.5° GFS grib files. In an earlier post complete GFS forecasts in grib2 format were downloaded and relevant fields extracted using the wgrib2 utility. In fact, it is possible to download only the required fields. This much faster partial-http option uses cURL and an easy to use Perl script called from NCEP.

jet.R is the script which produced the above graphics. Here Roger Bivand’s sp and rgdal packages are used to transform the latitude-longitude GFS projection to  a polar projection. For example, wind speeds in the northern hemisphere are contained in the SpatialGridDataFrame object sg_north. It is transformed into Universal Polar Stereographic (ups in the Proj.4 library) using
sg_north <- spTransform(sg, CRS("+proj=ups +north"))
sg_north@bbox <- polar_north@bbox

Unfortunately spTransform() produces a SpatialPoints object, because the grid is non-uniform after transformation. To recover a SpatialGrid object, the interp() function from package akima was used to resample back onto a regular grid. This is the slowest part of jet.R.