Sources of Error in NWP Forecasts

1. Sources of Error in NWP Forecasts or All the Excuses You’ll Ever Need Fred Carr COMAP Symposium 00-1 Monday, 13 December 1999

2. Introduction NWP has become an indispensable tool for the forecaster, but it is important to understand its limitations. There are many sources of possible error in an NWP forecast. If you keep these sources in mind as you examine NWP products, you should be able to make more intelligent use of the products in your forecasts. These sources of error can be grouped into three categories: A. Errors in the Initial Conditions It is a complicated process to collect data from observations and get them into a form that an NWP model can use. Errors can occur at several steps along the way, as well as grow out of limitations of the data sources themselves.

3. Errors in the Initial Conditions Observational Data Coverage Spatial Density Temporal Frequency Errors in the Data Instrument Errors Representativeness Errors Errors in Quality Control Errors in Objective Analysis Errors in Data Assimilation Missing Variables Errors in the Models Equations of Motion Incomplete Errors in Numerical Approximations Horizontal Resolution Vertical Resolution Time Integration Procedure Boundary Conditions Horizontal Vertical Terrain Physical Processes Precipitation Stratiform Precipitation ii Convective Precipitation Radiation Surface Energy Balance Boundary Layer Surface Layer ii Ekman or Mixed Layer Intrinsic Predictability Limitations Intrinsic Predictability Limitations

4. Introduction B. Errors in the Model A model is by definition an approximation of reality, and although NWP models continue to grow in complexity, they cannot take into account all factors that affect the weather. The numerical solution of these models by computers introduces additional error. C. Intrinsic Predictability Limitations Even with error-free observations and a “perfect” model, forecast error will grow with time. There is an intrinsic limit to the range of a useful forecast. This range is short for small-scale phenomena and increases for synoptic and planetary-scale features.

5. Errors in the Initial Conditions Observational Data Coverage Spatial Density Temporal Frequency Errors in the Data Instrument Errors Representativeness Errors Errors in Quality Control Errors in Objective Analysis Errors in Data Assimilation Missing Variables Errors in the Models Equations of Motion Incomplete Errors in Numerical Approximations Horizontal Resolution Vertical Resolution Time Integration Procedure Boundary Conditions Horizontal Vertical Terrain Physical Processes Precipitation Stratiform Precipitation ii Convective Precipitation Radiation Surface Energy Balance Boundary Layer Surface Layer ii Ekman or Mixed Layer Intrinsic Predictability Limitations Intrinsic Predictability Limitations

6. Intrinsic Predictability Limitations • Even with error-free observations and a “perfect” model, forecast errors will grow with time. • No matter what resolution of observations is used, there are always unmeasured scales of motion. The energy in these scales transfers both up and down scale. The upward transfer of energy from scales less than the observing resolution represents an energy source for larger-scale motions in the atmosphere that will not be present in the numerical model. Thus, the real atmosphere and the atmosphere that is represented in the numerical model are different. For this reason, the model forecast and the real atmosphere will diverge with time. This error growth is roughly equal to a doubling of error every 2-3 days. Therefore, even very small initial errors can result in major errors for a long-range forecast. • The problem just stated is the essence of chaos theory applied to meteorology. This theory proposes that nothing is entirely predictable, that even very small perturbations in a system result in unpredictable changes in time.

7. This graphic illustrates the effect of intrinsic predictability limitations on forecast skill. Forecasts based on climatology will have a relatively high level of error, but will remain constant over time. Forecasts based on persistence (i.e., whatever is happening now will happen later) are nearly perfect at extremely short range, but quickly deteriorate. Current models do well at short ranges, but eventually do worse than climatology. A forecast that is worse than climatology is considered useless. Intrinsic Predictability Limitations

8. Even the best model we can envision will, for reasons just discussed, produce forecasts that deteriorate over time to a quality lower than those based on climatology. Our current forecast models have skill up to the 5-7 day range on the synoptic scale for 500 hPa heights. (Occasionally they have skill at 15-30 days for time-averaged planetary waves.) They show much less skill for derived quantities such as vorticity advection or precipitation. Intrinsic Predictability Limitations

9. Intrinsic Predictability Limitations • A related predictability limitation is that intrinsic error growth will contaminate smaller scales faster than larger scales. In other words, a small-scale phenomenon will be less well forecast than a large-scale phenomenon in the same range forecast. • However, mesoscale/convective scale predictability may not follow this smooth progression due to its highly intermittent nature. For example, a rotating supercell thunderstorm may have more predictability (2-6 hr) than an airmass thunderstorm (1 hr). Topographically and/or diurnally-forced circulations such as drylines and sea breezes are more predictable than squall lines.

10. Concluding Comment • It used to be thought that the errors due to horizontal resolution constituted about 30% of the total forecast error. However, due to faster computers (which have allowed more accurate numerical schemes and higher resolution) this is no longer the case. • Currently, the largest source of error is more likely to be the unavailability of high resolution data over the entire forecast domain. One might now say that new (and accurate) observing systems, which measure the variables we need under all weather conditions, are the best way to improve NWP forecasts. Improvements in computers (which may allow higher horizontal and vertical resolution) and in the parameterizations of physical processes within the models will help, but to a lesser degree than new observing systems.