Different statistical downscaling techniques are tested for a forecasting procedure of the Local 3 Month Precipitation Outlook (L3MPO). The first technique being tested is the methodology used for the L3MTO that (1) applies a linear regression to identify the statistical relationship between a station parameter and its corresponding forecast region and (2) adjusts the regression parameters to the most recent trends at the station. We modified the original L3MTO linear regression methodology to account for the fact that precipitation is a discrete variable (either precipitation occurs or not), by treating it as a continuous variable being bounded at zero. The modification includes the use of a one parametric regression model by setting the intercept to zero. Such modification, in theory, should increase the standard error of predictions because the degree of freedom increases, due to the fact that fewer parameters are being estimated. Therefore, the L3MPO methodology has been evaluated by a verification analysis that used L3MPO hind-casts created using the archived forecast data from CPC's national outlooks for 232 sites in the western U.S. The Heidke skill score (HSS) at 75% confidence level is used as verification in this assessment of long-term forecast goodness. The HSS was computed for each station using 11 years (1994-2005) and all leads for individual target 3-month periods: e.g. January through March, February through April, etc. The stations were then stratified by two criteria: 1) existence of potential predictability and 2) conditions favoring assumption of Normal distribution. Overall, there are about 60% of stations that show forecast improvement over the use of the1971-2000 climatology. Forecasts were poor for only 10% of stations within the areas with existing potential predictability, whose data did not allow for the assumption of a Normal distribution. The forecast for such stations might improve if an alternative method to linear regression will be used.
The alternative methodology makes use of a regression model with a normal-quantile transformation of the data. The transformation includes the use of the 1971-2000 climatological underlying distribution (Normal, Lognormal or Gamma) expressed as normal quantiles. The prediction is made in the units of the normal quantiles that are translated to metric units using the climatology distribution. The advantage of using this method avoids the problems associated with the asymmetric properties of precipitation distribution. However, this methodology also has a disadvantage because of its inability to adjust for the most recent trends, which might play an important role in forecasting precipitation in a changing climate.
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