Smaller Spatial Scales

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Smaller spatial scale features developed in regional models are attributed to four types of sources: (1) the surface forcing, (2) the nonlinearities presented in the atmospheric dynamical equations, (3) hydrodynamic instabilities, and (4) the noise generated at the lateral boundaries and model errors. A better representation of small scale forcings such as topography and other surface heterogeneities (type 1) contributes to the increase of details in high-resolution simulations. The nonlinear dynamics (type 2) also play an important role. Internal atmospheric dynamics exhibits a nonlinear downscale cascade by stirring and stretching the flow, and this phenomenon would occur even in the absence of surface forcings. Shear and buoyancy in the flow can also, through hydrodynamic instabilities (type 3), produce mesoscale features without the help of surface forcings. The high resolution used by RCMs allows for a better representation of these three types of sources, in addition to the increased accuracy of the numerical scheme employed to solve the governing equations of the climate system. However, the noise introduced at the lateral boundaries and the model errors (type 4) may contaminate the simulations and forecasts.

Typical spectral distributions of the global model and the regional model are shown in Fig. 2.1 (Chen et al. 1999). After a relatively flat planetary wave portion of the kinetic energy spectrum, the global model shows a rapid drop-off with the -3 power law of geostrophic motion (Phillips 1963). Because of the strong artificial small-scale diffusion, an even more rapid drop-off occurs near the end of the global model resolution (i.e. T62 in this case) due to the strong small-scale diffusive damping in the model. The kinetic energy spectrum of the regional model is projected to the global zonal wave number. The regional model simulation with higher resolution continues to follow the -3 power drop-off until the end of the regional model resolution (i.e. wave 300 in this case), when another diffusion induced rapid drop-off occurs. The added value of the regional model in this case is that it can resolve the waves with wave numbers 30-300.

Over lands, denser grid spacing in regional models obviously improves the resolution of the terrain, and better represents the land use (type 1 of the sources). The surface forcing is thought to be the one that RCMs exploit the most because of heterogeneity of the land surface. An example is shown in Fig. 2.2. The climatology of precipitation over Kenya for observations is compared with that from an ensemble of three GCM runs at T42 spectral truncation (approximately 2.8 degrees resolution) and a nested regional model at 80 km and 20 km resolution, respectively. The GCM is the ECHAM GCM developed at Max Planck Institute for Meteorology (MPI, Roeckner et al. 1996),

Fig. 2.1. Regional (dashed line) and global (thin solid line) model kinetic energy (KE) spectra for January 1993. The global model spectral are only averaged over the latitude bands covering the regional domain, while the regional spectra are projected over to the global with respect to global zonal wavenumber (actually m + 1 so that the m = 0 can be included on this logarithmic plot). The thick solid line represents a theoretically predicted energy cascade curve (Chen et al. 1999)

and the regional model is the regional spectral model (RSM) developed at National Centers for Environmental Prediction (NCEP) (Juang and Kanamitsu 1994). The observations are interpolated to 20 km x 20 km grids using 453 station data. The GCM cannot resolve the observed local precipitation maxima around Lake Victoria and over Kenya highland. The regional model at 80 km resolution can "see" Lake Victoria (i.e. 15 grids on Lake Victoria), and produces the local precipitation maximum around the lake. But it fails to generate the local precipitation maximum over Kenya highland because the horizontal gradient of the terrain at 80 km resolution is not strong enough. The regional model at 20 km resolution represented Lake Victoria well with more than 200 grids, and raises the height of Kenya highland by approximately 2 000 meters higher compared to the GCM, thus significantly increases the horizontal gradient of the terrain relative to the GCM. As expected, it is able to generate the two observed local precipitation maxima.

Over oceans, denser grid spacing in regional models mainly exploits the types 2 and 3 of the sources (list in first paragraph of this section). A typical tropical cyclone in the regional model and the global model are illustrated in Figs. 2.3 and 2.4, respectively. The GCM resolution is about 280 km and the regional model resolution is 50 km. Higher resolution leads to a much finer representation of the 850 hPa vorticity in the regional model compared to the driving GCM. The maximum vorticity near the center of the storm is much higher than that of the driving GCM. The maximum wind speed is higher in the regional model, and there is a clear minimum near the center of the storm, an attempt by the regional model to produce the storm's "eye." Precipitation and humidity values are also higher in the regional model, and there appears to be a rain band that is not present in the GCM simulation. Therefore, the high-resolu-

Fig. 2.2. October-November-December precipitation averaged for 1970-1995; a observation; b ECHAM GCM ensemble mean; c ensemble mean of the ECHAM-RSM first nesting (resolution of 80 km); d ensemble mean of ECHAM-RSM double nesting (resolution of 20 km). The precipitation unit is mm day-1

tion regional model gives a representation of the tropical cyclone that is much more similar to the reality than that obtained by a coarse global model.

To date, it is widely accepted that dynamical downscaling improves spatial patterns and climatologies as compared to the coarse resolution GCMs.

140° E 150° E 160° E 140° E 150° E 160° E

Fig. 2.3. Typical fields of a tropical cyclone in the regional model; a vorticity at 850 hPa (xio-4 s-1); b wind speed at 1000 hPa (m s-1); c precipitation (mm per 6 hours); d specific humidity at 850 hPa (g kg-1) at 14 June 1994 00:00 GMT (Camargo et al. 2007)

Fig. 2.3. Typical fields of a tropical cyclone in the regional model; a vorticity at 850 hPa (xio-4 s-1); b wind speed at 1000 hPa (m s-1); c precipitation (mm per 6 hours); d specific humidity at 850 hPa (g kg-1) at 14 June 1994 00:00 GMT (Camargo et al. 2007)

Predictability at Smaller Spatial and Temporal Scales

Dynamical downscaling has been performed in many regions (e.g. Castro et al. 2005; Misra et al. 2003; Roads et al. 2003; Sun et al. 1999a,b). Most of these investigations are case studies (e.g. simulations of wet and dry years or warm and cold years). To answer the question of whether predictability of climate systems is improved by dynamical downscaling is to use multiple GCMs with multiple ensembles and force multiple regional models (Leung et al. 2003). This task exceeds our current computational limits, and has not been accomplished for any regions yet. An attempt is made to shed light on this by the 30-year multiple ensembles of one GCM, the ECHAM4.5 GCM (T42), and one RCM, the RSM, with resolution of 60 km for northeast Brazil (the Nordeste) (Sun et al. 2005). The primary objectives are to find out: (1) whether the finer spatial scale information produced in the regional model is skillful, or is it just 'noise' on top of the large-scale signal? and (2) whether the temporal character of variability is skillful in the regional model?

A spatial scale separation technique is applied to analyze the added value of the RCM compared with the GCM. The observed and RCM simulated precipitation is

Fig. 2.4. Typical fields of a tropical cyclone in the global model; a vorticity at 850 hPa (xio-4 s-1); b wind speed at 1000 hPa (m s-1); c precipitation (mm per 6 hours); d specific humidity at 850 hPa (g kg-1) at 14 June 1994 oo:00 GMT (Camargo et al. 2007)

upscaled to the GCM resolution (i.e. about 2.8 degrees). This is done by using running average over 5 x 5 RCM gridpoints. The upscaled precipitation is treated as the large-scale component, and the precipitation difference between the total field and the large-scale component is treated as the local component. There is no local scale component in the GCM simulations. The local scale component accounts for a small portion of total precipitation climatology (e.g. about 15% averaged over Ceara, Brazil). However, it significantly contributes to the total precipitation variability. The standard deviation of the observed local scale component is roughly one-half of that of the observed total precipitation. The RCM has the ability in producing variability of the local component. It can generate about one-half of the observed variations of the local scale component of precipitation in Ceara.

The physical climate anomaly signal in both RCM simulations and observed precipitation data tend to be contaminated by noise, particularly for the local scale component. In order to separate the signal from the noise, both observed and RCM simulated local scale component of precipitation are filtered by retaining only the leading empirical orthogonal function (EOF). Figures 2.5 and 2.6 illustrate the observed and simulated leading EOF patterns, as well as the corresponding principal components, respectively. Compared with the observed leading eigenvector (EOF1), the RCM

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Fig. 2.5. The leading EOF patterns for local scale component of precipitation for the period February-March-April 1971-2000 in Ceara; a observation; b NCEP RSM simulation. The contours show the actual eigenvector values multiplied by 10. Contour interval is 0.5 (Sun et al. 2005)

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Fig. 2.5. The leading EOF patterns for local scale component of precipitation for the period February-March-April 1971-2000 in Ceara; a observation; b NCEP RSM simulation. The contours show the actual eigenvector values multiplied by 10. Contour interval is 0.5 (Sun et al. 2005)

captures the general patterns of the observations: positive amplitude along the coastal areas and southern Ceara, and negative amplitude in central Ceara. The leading EOF of the observation explains about 17% of the total variance, while the explained variance for the leading EOF of the RSM is much higher (47%). As shown in Fig. 2.6, the time series of the leading EOF between the observations and RSM simulations are in good agreement, with a correlation coefficient of r = 0.44.

Predictability of local scale component can also be revealed by ensemble mean contingency tables. Contingency tables for coastal, central and southern Ceara are given in Table 2.1. They indicate that the regional model has reasonable skill for the local scale rainfall. For instance, it is 5 of 10 years when the RCM indicated below-normal (above-normal) local scale rainfall and the location was observed to receive below-normal (above-normal) local scale rainfall in the coastal Ceara.

An aspect of precipitation variability that is important for climate impact assessments is the distribution of daily precipitation through the season, which can be as important, or even more important, than the seasonal average precipitation. Studies that concern weather analysis in climate models are relatively few. Previous studies indicated errors of too high and too low daily variability of precipitation in GCMs (Mearns et al. 1990). GCMs missed important aspects of the ENSO signal in seasonal statistics of daily precipitation although they are capable of capturing the ENSO signal in seasonal averaged precipitation (Gershunov and Barnett 1998). The analysis of daily precipitation in GCMs is probably of limited value, given the crude horizontal resolution (e.g. the GCM cannot resolve important topographic influences on precipi-

Fig. 2.6. Time series of the leading EOF mode for local scale component of precipitation (Sun et al. 2005)
Table 2.1. Ensemble mean contingency tables for FMA season; a coastal Ceara; b central Ceara; c southern Ceara. Categories of model ensemble mean are listed across rows and observed categories are listed down columns

a

OBS

Coast

B

N

A

RSM

B

5

3

2

N

3

4

3

A

2

3

5

b

OBS

Central

B

N

A

RSM

B

5

2

3

N

4

5

1

A

1

3

6

c

OBS

Southern

B

N

A

RSM

B

4

3

3

N

3

5

2

A

3

2

5

tation, nor synoptic scale precipitation processes) and the crude parameterizations of precipitation. However, the model parameterization schemes are steadily improving, and regional models have relatively fine horizontal resolutions. This mitigates some of the limitations of GCMs, and examination of daily precipitation may prove more fruitful. Over northeast Brazil, the RSM shows reasonable skill in producing the interannual variability of daily precipitation intensity distribution (Sun et al. 2005). The RSM has measurable skill in capturing the variability of dry spells as well. Sun et al. (2007) defined a drought index (D) to measure the severity of drought conditions.

where n is the total number of dry spells during the season, Li is the length of the ¿th dry spell in days. A dry spell is defined as three or more consecutive days with daily precipitation of less than 2 mm.

The weight (W) is a function of the length of dry spells. Calibration has been done to obtain the optimum values of the weight. A strong weight (W) is given to dry spells longer than 9 days because of the severe damage to crop yields in this region.

The regional model simulates the observed drought index well (Fig. 2.7). Examination of the relationship between the seasonal mean precipitation and the drought index indicates that, (1) the drought index is closely associated with the seasonal mean precipitation only when the drought index is extremely high or low (i.e. the drought index is at least one standard deviation higher or lower than the average), and (2) the drought index is essentially not correlated to the seasonal mean precipitation when the drought index variance is less than one standard deviation. Thus, the drought index can not be derived from the seasonal mean precipitation, and can be treated as an independent variable except for the years with extreme anomalies.

The interannual variability for the drought index is higher than that for the seasonal mean precipitation. The standard deviation-to-mean ratio is 40% (43%) for observed (RCM simulated) seasonal mean precipitation, and 77% (66%) for observed (RCM simulated) drought index. This higher variability provides further evidence of the meaningfulness of the drought index as compared to the seasonal total precipitation.

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