Seasonal Predictions Using a Regional Spectral Model Embedded within a Coupled Ocean–Atmosphere Model

S. Cocke Center for Ocean–Atmospheric Prediction Studies, The Florida State University, Tallahassee, Florida

Search for other papers by S. Cocke in
Current site
Google Scholar
PubMed
Close
and
T. E. LaRow Center for Ocean–Atmospheric Prediction Studies, The Florida State University, Tallahassee, Florida

Search for other papers by T. E. LaRow in
Current site
Google Scholar
PubMed
Close
Full access

Abstract

This paper describes a new climate model and its potential application to the study of ENSO impacts. The model is a regional spectral model embedded within a global coupled ocean–atmosphere model. The atmospheric part of the model consists of a global spectral model with triangular truncation T63 and a nested regional spectral model. The regional model is a relocatable spectral perturbation model that can be run at any horizontal resolution. In this paper the regional model was run with a resolution of 40 km. The global atmosphere model is coupled to the Max Planck global ocean model. No flux correction or anomaly coupling is used.

An ensemble of 120-day integrations was conducted using the coupled nested system for the boreal winters of 1987 and 1988. A control integration was also performed in which observed SSTs were used in both the global and regional models. Two domains were chosen for the regional model: the southeast United States and western North America.

Results from the global models show that the models reproduce many of the large-scale ENSO climate variations including the shifts in the Pacific ITCZ and SPCZ along with a Pacific–North America response in the 500-hPa height field. These results are compared against the corresponding ECMWF and Global Precipitation Climatology Centre analysis. Over the southeast United States both the global and regional models captured the precipitation variations between the two years as compared with the monthly mean cooperative station data. It is shown that the regional model solution is consistent with the global model solution, but with more realistic detail. Finally prospects for using this coupled nested ocean–atmosphere regional spectral model for downscaling are discussed.

Corresponding author address: Dr. Steven Cocke, Center for Ocean–Atmospheric Prediction Studies, The Florida State University, 205 Johnson Bldg., Tallahassee, FL 32306-2840.

Email: steve@monsoon.met.fsu.edu

Abstract

This paper describes a new climate model and its potential application to the study of ENSO impacts. The model is a regional spectral model embedded within a global coupled ocean–atmosphere model. The atmospheric part of the model consists of a global spectral model with triangular truncation T63 and a nested regional spectral model. The regional model is a relocatable spectral perturbation model that can be run at any horizontal resolution. In this paper the regional model was run with a resolution of 40 km. The global atmosphere model is coupled to the Max Planck global ocean model. No flux correction or anomaly coupling is used.

An ensemble of 120-day integrations was conducted using the coupled nested system for the boreal winters of 1987 and 1988. A control integration was also performed in which observed SSTs were used in both the global and regional models. Two domains were chosen for the regional model: the southeast United States and western North America.

Results from the global models show that the models reproduce many of the large-scale ENSO climate variations including the shifts in the Pacific ITCZ and SPCZ along with a Pacific–North America response in the 500-hPa height field. These results are compared against the corresponding ECMWF and Global Precipitation Climatology Centre analysis. Over the southeast United States both the global and regional models captured the precipitation variations between the two years as compared with the monthly mean cooperative station data. It is shown that the regional model solution is consistent with the global model solution, but with more realistic detail. Finally prospects for using this coupled nested ocean–atmosphere regional spectral model for downscaling are discussed.

Corresponding author address: Dr. Steven Cocke, Center for Ocean–Atmospheric Prediction Studies, The Florida State University, 205 Johnson Bldg., Tallahassee, FL 32306-2840.

Email: steve@monsoon.met.fsu.edu

1. Introduction

Regional models are becoming increasingly popular for simulating regional climates. High-resolution regional models are capable of resolving more accurately regional variations in the orography and land surface characteristics that are important for regional climate simulation. The earliest extended regional simulations were for periods of only a few days (Dickinson et al. 1989). Since then other investigators have developed regional models for climate studies. These models are typically high-resolution limited area gridpoint models that are coupled to coarse resolution GCMs or analyses. These models have been used to simulate individual monthly climatologies resulting from a doubling of the atmospheric carbon dioxide concentrations or sensitivity results from tropical deforestation. Recently they have been used with varying degrees of success to study monsoons and climate variability. Recent reviews of regional climate modeling techniques and studies are presented in McGregor et al. (1993), McGregor (1997), and Giorgi (1995).

Most regional models, and virtually all regional climate models, to date have been gridpoint (finite difference) models. However, there have been a number of novel attempts at using the spectral method in limited domain, short-range forecasting. The advantages of the spectral method are well known: absence of computational phase and aliasing errors, high-order accuracy in computing derivatives, ease of implementing semi-implicit time integration, and horizontal diffusion. The difficulty of using the spectral technique comes from formulating the lateral boundary condition. Tatsumi (1986) developed a regional spectral model that uses double Fourier sine–cosine series with additional sinusoidal (nonorthogonal) terms added to satisfy the lateral boundary conditions. The superiority of the spectral method over finite differencing was demonstrated by Tatsumi (1986). Other attempts at regional spectral modeling include Fulton and Schubert (1987a,b) who use Chebyshev polynomials. Chen and Kuo (1992a,b) and Chen et al. (1997) use harmonic-sine series. The spectral High Resolution Limited Area Model uses double Fourier series with an extension zone beyond the lateral boundaries to handle the periodicity of the basis functions (Haugen and Machenhauer 1993).

Another approach to regional modeling is to use a perturbation technique. In these types of models, the large-scale information is passed throughout the regional domain, rather than just at the lateral boundaries. One such model is the spectral boundary coupling (SBC) method of Kida et al. (1991). In the SBC method, the long-wave components of the regional model are replaced by the corresponding long-wave components of the driving model at specified time intervals. The short-wave components are obtained by subtracting the regional fields from the long-wave components and are not represented by spectral functions. Yet another approach is that used in nested regional spectral models such as the European Centre for Medium-Range Weather Forecasts (ECMWF) Spectral Limited Area Model (Hoyer 1987), the National Centers for Environmental Prediction (NCEP) regional spectral model (Juang and Kanamitsu 1994), and the model that we present here, the Florida State University Nested Regional Spectral Model (FSUNRSM) (Cocke 1998). In these models, finer-scale perturbations to a coarser global model are forecast. The perturbations are represented by spectral functions. Note that in the nested regional spectral method, the perturbations can develop long-wave components (i.e., long with respect to the regional domain size), which is quite different from the SBC method where the long-wave components are replaced. Thus the SBC method provides a stronger constraint on the regional model solution. Another significant difference between the SBC method and the nested regional spectral method is that the latter utilizes the spectral technique for calculating the horizontal derivatives, solving the semi-implicit time integration scheme and horizontal diffusion. The advantage of the perturbation method is that the global model forecasts the large- (planetary-) scale flow, which cannot be well represented in a limited domain. The ability to handle the large-scale flow well in a limited domain is especially important for regional climate modeling.

A promising and as yet unexplored area for regional climate modeling lies in prediction of El Niño–Southern Oscillation regional impacts. This has been brought about by the fact that coupled ocean–atmosphere models are beginning to consistently show skill in predicting tropical Pacific sea surface temperature (SST) anomalies associated with ENSO events at lead times of one year (Latif et al. 1994). Additionally, the atmospheric general circulation components of these coupled systems are able to simulate global circulation patterns associated with the ENSO SST anomalies. At present these atmospheric GCMs are too coarse to resolve in detail any regional impacts associated with local variations in the topography or land surface. However, the perturbation regional model, using the global model solution as a base, in principal will be able to use all the information gained from the coupled models and make more detailed predictions of regional ENSO impacts. The finer detail from the regional model will be better suited for use in downscaling models, such as crop or river basin models.

In this paper, we present the FSU Nested Regional Spectral Model and coupled ocean–atmospheric model system and its potential application to the study of ENSO impacts by examining the warm and cold events in 1987–89. The regional domain was centered in the southeast United States where a strong precipitation signal is observed in the boreal winter months. To show the enhancements due to the improved orography the regional model was relocated to the western United States for the boreal winter of 1987. Since the FSUNRSM is a relatively new model, we discuss it in some detail in section 2. The FSU coupled model (LaRow and Krishnamurti 1998) that the FSUNRSM is nested in is described in section 3. The experimental setup is described in section 4. Sections 5 and 6 present results from the FSU coupled model. Section 6 presents results from the regional model over the southeast and western United States. A summary and conclusions are given in section 7.

2. Nested regional spectral model

A nested regional spectral model has recently been developed at FSU and was first used in hurricane prediction studies (Cocke 1998). The model has undergone considerable enhancement to enable it to be used for seasonal and longer-term simulations. The model uses a perturbation method that is similar to that used at NCEP (Juang and Kanamitsu 1994) and ECMWF (Hoyer 1987). There are some differences, however. For example, the FSUNRSM uses spectrally rotatable Mercator map projection, which allows the use of the same dynamics code for the regional and global models. The boundary relaxation is somewhat different, in particular the FSUNRSM does not use blending at the lateral boundaries. In order to compute the perturbation tendencies, it is necessary to obtain the global model time tendencies on the regional grid. The FSUNRSM uses an inverse semi-implicit algorithm rather than just a simple temporal finite difference to obtain these tendencies. There are other differences that we cannot readily determine based on what has been published in the literature.

As mentioned above, the regional model predicts fine-scale perturbations to the FSU global model solution; that is, the regional model solution is the global solution plus the perturbations. These perturbations are spectrally represented by pi-periodic trigonometric series and are relaxed at the lateral boundaries so that the regional fields approach the global model solution. Only the perturbations are spectrally analyzed in the regional model, not the full regional fields themselves. Depending on the variable, the perturbations satisfy a zero or mirror boundary condition. The advantage of the perturbation technique is that the large-scale flow that is not well resolved by the regional model is predicted by the global model, and the finer-to-intermediate scales are forecast by the regional model. In most other regional models, the large-scale flow is passed into the regional domain through a narrow blending or relaxation zone, typically a few grid points in width, at the lateral boundaries. The perturbation method naturally incorporates the large-scale flow throughout the regional domain. This should be particularly beneficial for long-term integrations, such as climate simulations.

a. Basic method

The regional fields are the sum of the global model solution and the perturbation field. The global model is run first, and the output global fields are then spectrally transformed to the regional grid at a regular (nest) interval, typically every 3 to 6 h. The use of a spectral transformation eliminates the need for horizontal interpolation, thus reducing error. These fields are then linearly interpolated in time to the time steps of the regional model. At each time step, the perturbations are added to the global fields to obtain the full regional fields, and the nonlinear dynamical and physical tendencies are computed. The perturbation time tendencies are obtained by subtracting the regional time tendencies from the global time tendencies. The perturbation tendencies are then spectrally analyzed, and the perturbations at the next time step are then solved using a semi-implicit time integration scheme. Currently, only one-way nesting is done; the regional solution does not feed back into the global model.

b. Map projection

We use a Mercator projection for the regional grid. The transformation of the north–south coordinate is given by
i1520-0493-128-3-689-e1
where θ is the latitude in spherical coordinates. The east–west coordinate, x, is the same as the spherical longitudinal coordinate, λ. The inverse transformation is easily obtained. For regional domains near the equator, the Mercator grid is nearly regularly spaced and hence there is very little grid distortion. For domains at higher latitudes, a coordinate rotation is performed so the regional domain is placed at the new equator. If a global variable, A, is represented by a triangularly truncated basis of spherical harmonics, this rotation can be done spectrally via
i1520-0493-128-3-689-e2
where dlmn(θrot) are rotation matrix elements that can be found in many quantum mechanics texts. For triangular truncation, there is no loss of information due to this rotation. While dlmn(θrot) can in principle be found through summation formulas (see, e.g., Brink and Satchler 1979), for high wavenumbers this direct summation can lead to significant numerical roundoff errors. To overcome this, we have developed a fast and accurate recursion relation to compute the rotation matrix elements.

While a number of conformal map projections could be used, the Mercator projection offers a possibly significant computational advantage. Since the Mercator longitudinal coordinate is the same as the spherical longitudinal coordinate, a fast-Fourier Legendre transform can be used to project the global variables onto the regional grid. For frequent nesting this could result in substantial savings, depending on domain size and resolution.

c. Model equations

The model equations are solved using a semi-implicit leapfrog time integration scheme. The equations for the perturbations may be written
i1520-0493-128-3-689-e3
where ′, ζ̃ are the perturbation divergence and vorticity scaled by the map factor, mF. The variables q′, S′ are the perturbation log surface pressure and specific humidity, respectively; P′ = Φ′ + RT*q′, where Φ′ is the perturbation geopotential height, R is the gas constant; and T* = 300 K. Variables with subscript g are global variables. The time-differencing operator is δt and variables with an overbar are time averaged. The map factor is linearized so that mF = m0 + m′, where m0 is the domain average of mF. The operators A, I are second-order vertical finite differencing and vertical finite integration operators. The terms RHSD, RHSζ, RHSP, RHSq, and RHSS are the nonlinear terms from the primitive equations. Details of these terms and derivation of these equations are given in appendix A.
The equations can be written in spectral form as
i1520-0493-128-3-689-e8
where RHSD′, RHSP′, RHSζ′, RHSq′, and RHSS′ are the right-hand sides of the perturbation equations and are computed explicitly on the transform grid. The solution for the spectral coefficients is relatively straightforward and is done in exactly the same manner as in the global spectral model (Krishnamurti et al. 1998).

d. Orography and lateral boundary relaxation

A finer orography is included in the regional model by means of a perturbation orography Φs. This term is included via the perturbation variable P′ = Φ′ + RT*q′, where Φ′ = Φs + σ1RTd lnσ. The perturbation orography is blended at the lateral boundaries to the global model orography.

A simple method is used to relax the perturbation variables to zero at the lateral boundaries. To each tendency equation an extra term is added so that
i1520-0493-128-3-689-e13
where α → 0 in the interior of the regional domain, ατ−1 near the lateral boundaries, and τ is the relaxation time, typically on the order of 1 h. Generally α is very small or zero throughout most of the interior so that relaxation is only effective near the lateral boundaries. If the perturbation orography is significantly different from zero near the lateral boundary, a reference term Aref may be added to the temperature and pressure tendency equations in order to prevent overrelaxation of these variables so that they do not become inconsistent with the perturbation orography. Generally it is probably best to sufficiently blend the regional and global orographies at the boundaries so that Aref can be set to zero.

e. Spectral representation and truncation

The perturbation variables are expanded in a set of basis functions consisting of pi-periodic sine or cosine series
i1520-0493-128-3-689-e14
where f, g are sin or cos and I, J are the number of grid points in the x, y direction. The choice of sin or cos depends on the variable. The cosine functions satisfy a mirror (symmetric reflection) boundary condition and are used for the variables ′, T′, S′, and q′ in both horizontal directions. This choice of representation for ′ means that we should use a sin–cos (i.e., sin in the x direction, cos in the y direction) representation for the u′ wind component and a cos–sin series for υ′ since ′ = ∂u′/∂x + ∂υ′/∂y. The vorticity, ζ̃, is thus represented by a sin–sin series.

The spectral series given above is truncated to remove aliased terms of cubic or higher order, as in the global spectral model. However, the presence of the map factor in the primitive equations above results in some cubic terms, particularly for the advection terms. We do not take these terms into account in the truncation, so there will be some aliasing. This aliasing can be minimized by rotating the grid toward the equator where the map factor is nearly constant.

We have implemented a choice of either rectangular or elliptic truncation. With rectangular truncation all unaliased east–west and north–south modes are kept. The truncation is given by
i1520-0493-128-3-689-e15
Elliptic truncation is isotropic, and thus only those modes (m, n) that satisfy
i1520-0493-128-3-689-eq1
are kept.

f. Model physics

The regional and global models share the same physics. We include long- and shortwave radiation, including the effects of clouds. For computational economy, the radiation calculations are performed every three hours in the global model and every hour in the regional. Boundary layer processes such as sensible heat, latent heat, and momentum flux are parameterized using bulk aerodynamic theory coupled to similiarity theory. For surface evaporation, the latent heat flux includes a ground wetness parameter, which can be a function of the albedo, accumulated rain, and terrain. Surface temperatures are calculated using an energy balance equation. This method seems to produce a reasonable diurnal cycle but with somewhat cooler than observed nightime temperatures. The cold bias is partly due to lack of a deep soil reservoir in the current scheme. Details of the model physics can be found in Krishnamurti et al. (1991). However, we are near completion in implementing a detailed biosphere model, a variation of the Biosphere–Atmosphere Transfer Scheme (Dickinson et al. 1993).

We have implemented a choice of either an enhanced Kuo convection scheme or a simplified Arakawa–Schubert scheme. The enhanced Kuo scheme is based on the modified Kuo scheme of Krishnamurti et al. (1983). Enhancements include using a generalized structure function for the vertical heating and moistening profile. This enables us to tune the Kuo scheme to a profile that is closer to observations, especially in a mean sense. This minimizes climatological drifts due particularly to excessive heating at the upper levels by the old Kuo scheme. The Arakawa–Schubert scheme was adapted from a version developed by Pan and Wu (1994) that is now used in the operational Medium-Range Forecast (MRF) model at NCEP. A comparison of the two schemes is in progress. A summary of the physics is given in the appendix B.

g. Computational aspects

Both the global and regional models have been developed to take advantage of scalable parallel architectures. The grid calculations are done using a domain decomposition approach. When a small number of processors are used, the domain decomposition is simply a one-dimensional partitioning of the latitude bands. Each latitude band may be arbitrarily assigned to any processor to achieve optimal load balance, but a simple consecutive partitioning is usually sufficient. The vertical calculations for any given domain are done on the same processor. For a large number of processors, a two-dimensional decomposition of the horizontal is used. The spectral transforms are done using a transpose Fourier–Legendre (for global model) or transpose double Fourier (regional model) parallel algorithm.

3. Coupled ocean–atmosphere model

The atmospheric component of the coupled system is a version of the Florida State University Global Spectral Model. The model is truncated at horizontal resolution of 63 waves, which corresponds to approximately 1.875° by 1.875° in the Tropics. The vertical structure consists of 14 unevenly spaced vertical levels. The model physics employs the same physics as the regional model (see appendix B).

The primitive equation ocean model is a slightly modified version of the Max Planck Institute global ocean model originally developed by E. Maier-Reimer. The model has been used extensively for ENSO studies (e.g., Latif 1987; Barnett et al. 1991; LaRow and Krishnamurti 1998). The dynamically active domain extends from 50°N to 50°S and is global in the zonal direction. Outside of 50° latitude the model uses Newtonian relaxation on the salinity, temperature, and wind stress to prevent large model drift near the boundaries, which are located at 70°. The model does not include a sea ice model. The ocean model’s forcing includes freshwater, net heat, and momentum flux determined by the atmospheric model. The ocean model provides updated sea surface temperatures to the atmospheric model every ocean model time step (2 h). The global coupled model uses full coupling and does not employ flux correction or anomaly coupling. The fluxes derived from the atmospheric model are time averaged before being used by the ocean model to determine the new SSTs. In addition to being passed to the atmospheric GCM, the SSTs are averaged over each 24-h period during the coupled integration and are saved directly on the ocean model’s grid. The SSTs are then interpolated directly to the regional atmospheric model’s grid, thereby minimizing the loss of information from the high tropical resolution of the ocean model.

4. Experimental setup

Two 120-day experiments were conducted for the boreal winters (November–February) of 1987 and 1988. For each experiment the fully coupled GCM and a control (prescribed SSTs) were run. In order to quantify the results from the coupled model, a five-member ensemble was conducted for each year. Each ensemble member was 120 days with the atmospheric initial conditions chosen from consecutive start dates centered on 1 November. Output from each GCM experiment was used as input for the regional model. The regional model was centered on the southeastern United States.

In these experiments the regional model had an effective resolution of 40 km. The control experiment used Reynolds’ (1988) weekly averaged SSTs in both the global and regional models and were updated once a week. To examine the impact of influences of orography an additional integration was performed with the regional model centered over western North America. This experiment was only for the winter of 1987. The regional domains are shown in Fig. 1.

In order to reduce the coupling shock the coupled model was initialized in a two-step procedure. First, the ocean model was spun up for a period of 10 yr from a climatological base state to the respective starting dates of 1 November 1987 and 1 November 1988. During the spinup, the ocean model used as forcing the monthly mean SSTs from Reynolds and the FSU pseudo–wind stresses (Stricherz et al. 1992). Next, the atmospheric model was integrated for a period of 30 days using the final SSTs determined from the ocean spinup. During this phase the SSTs were held constant. This allowed the atmosphere to adjust to the SSTs and reduced the shock when the models are coupled. The final atmospheric state obtained after the 30-day fixed SST integration was then used as initial conditions for the coupled model. A similar initialization procedure was employed by Latif et al. (1993) to minimize drifts due to imbalances between model states.

The initial perturbations for the regional model variables including the orography was obtained using a T240 global model dataset. The Gaussian grid spacing for T240 is roughly 0.5°; thus, the regional model was initialized at close to its fullest resolution.

5. Results

The global model’s ability to simulate observed variability during the two seasonal integrations is discussed in the following sections. Since the regional model’s base fields are the solutions obtained by the global model, it is important for the global model to obtain realistic ENSO responses in order to minimize sources for errors in the regional model. Throughout the rest of the paper we use “differences” to indicate the period 1987 minus 1988 for the months of November and December and 1988 minus 1989 for the months January and February. All fields showing the coupled model and its regional integrations are the means from the ensembles.

a. Tropical Pacific SST difference

During 1987–88 the ENSO event in the Pacific swung from a warm event to a cold event. The November through January observed and predicted SST differences in the tropical Pacific are shown in Fig. 2b. The observed SSTs were 3 K warmer during 1987 along the equator from the date line to 120°W and extending in the latitudinal direction 5° off the equator. The characteristic horseshoe-shaped pattern with cold midlatitude anomalies encircling the equatorial warm anomalies are evident in the observed. The coupled model simulated this horseshoe-shaped pattern in the Pacific SST anomalies (Fig. 2a). The domain encompassed by the observed +1° anomalies was well simulated by the coupled model as was the −1° anomalies near 30°. In the east Pacific, south of the equator, the coupled model begins to show signs of premature cooling. This is not an uncommon problem with coupled GCMs. We have made several changes to the atmospheric model’s physics, many of which directly affect the coupling to the ocean model and possibly contributed to this drift. The most notable change to the physics was the switch to a mass flux closure cumulus convection scheme from the moisture convergence scheme of Kuo. This reduced the model’s tendency to generate “gridpoint” storms and the erroneous wind stresses that accompany those storms. Because of the increase in resolution and change in the cumulus parameterization the wind stresses are now stronger and better resolved near the equator. This has resulted in increased upwelling near the equator in the ocean model.

b. The 1988 minus 1989 January 500-hPa geopotential heights

This section examines the average January monthly Northern Hemisphere 500-hPa geopotential height differences generated by the two global models with those obtained from ECWMF analyses. It was during the boreal winter months that the two phases of this ENSO event achieved their highest amplitudes as measured by SST anomalies in the Niño-3 region. During the El Niño event of 1987 ECMWF analysis shows a deeper Aleutian low, intensification of the Canadian ridge, and lower heights over the southern United States (Fig. 3c). This pattern is similar to the classic positive phase of the Pacific–North American (PNA) pattern often associated with ENSO winters and is one of the largest Northern Hemisphere climate signals. Both the control and coupled model were able to simulate this PNA-like response (Figs. 3a,b). The coupled model with time-varying SSTs produced larger-amplitude height variations than either the control or the ECMWF analysis. These large height variations are in part due to slight phase differences between the solutions of the ensemble members. The coupled model also shows lower heights in the mid-Atlantic region in contrast to the ECMWF and control. The probable causes for these low heights over the mid-Atlantic region in the coupled model’s is due to the coarse resolution of the ocean model at these latitudes making it difficult to properly resolve the SST gradient and the cold continental air overrunning the relatively warm waters along the east coast of the United States. This caused an excessive amount of precipitation off the east coast of the United States extending out into the Atlantic in the coupled model (Fig. 6).

c. The 1988 minus 1989 January 850-hPa temperatures

Similar to the 500-hPa heights, both models simulated the correct location and magnitudes of the 850-hPa January temperature differences over the United States compared to the ECMWF analysis (Fig. 4). The eastern half of the United States is colder by 4°–6°C during January 1988 in both the ECMWF analysis and the coupled model. The control displaced the location of this temperature variation farther to the west near northern Mexico. In contrast to the eastern half of the United States, the western United States was warmer by 1°C during the warm event. This dipole pattern in the temperature field was simulated well by both the coupled model and the control, although both models simulated smaller positive values compared to the ECMWF analysis. During January, the largest amplitude signal in the ECMWF analysis is found over Alaska. Here large positive values close to 14 K are found in both the ECMWF analysis and in the coupled model but are absent in the control. The fact that this signal is absent from the control is somewhat surprising given the fact that the control used observed SSTs and contains the same physics as in the coupled model. Both the control and coupled model have difficulty in simulating the weak temperature gradients found in the ECMWF analysis at 850 hPa over northern Siberia. This is probably related to the insufficient parameterizations of snow and ground wetness in our model.

d. The 1987 minus 1988 November precipitation differences

The warm and cold phases of ENSO produce strong variations in precipitation around the globe. In particular, there is a significant correlation between the SST anomalies in the tropical eastern Pacific and wintertime precipitation over the United States. In this section comparisons are made with the global model’s November and January monthly mean precipitation differences with those from the Global Precipitation Climatology Centre (GPCC) (Huffman et al. 1997).

During November the control and coupled models show good agreement with the GPCC November differences (Fig. 5). The location and magnitude of the Pacific intertropical convergence zone (ITCZ) and South Pacific convergence zone (SPCZ) were well simulated by both models with each model simulating a southward displacement of the ITCZ and a northward displacement of the SPCZ during November 1987. Over North America, the coupled model simulated the precipitation differences in the Gulf of Mexico, over Texas, and in the southwest United States. The control model was able to simulate many of these differences; however, the control was unable to simulate the precipitation differences in the Gulf of Mexico. Examination of the 1987 and 1988 November 1000-hPa streamlines revealed that the control model did not simulate the northeasterly flow in this region during 1987 as observed in the ECMWF analysis and simulated by the coupled model. The control also simulated southerly flow over the Gulf of Mexico during November 1988 while the coupled model and ECMWF show a more easterly flow during the period. At this time it is difficult to say why the control, which represents the upper bounds for predictability, was unable to simulate the northerly flow. We speculate that a possible cause of the incorrect flow in the control is related to the frequency at which the SSTs were updated.

e. The 1988 minus 1989 January precipitation differences

During days 60 to 90 of the integrations, many of the global patterns noted in the GPCC analysis are again found in both the coupled and control model (Fig. 6). These features include the continuation of the equatorward displacement of the ITCZ in the Pacific along with increased precipitation in the Gulf of Mexico, southeastern, and western United States, and in northern Argentina during the warm event. Decreased precipitation amounts during January 1988 (w.r.t. 1989) are found over over the east-central United States extending from Texas to the Great Lakes region and over northern and southeastern Brazil.

Both global models simulate these shifts in the global precipitation patterns reasonably well. For example, the models simulated the increase in precipitation over the Gulf of Mexico and along the east and west coasts of North America. The models did however have some problems in simulating the increase in the precipitation over the central United States during January 1989. The equatorward displacement of the ITCZ in the Pacific continues to be simulated by the models; however, the coupled model’s ensemble mean is beginning to show a deterioration of the precipitation pattern in the tropical Pacific. The models also continue to simulate the variations in the SPCZ east of the date line, a feature noted by Janowiak and Arkin (1991).

Studies have shown that it is necessary to use a relatively large number (≥10 members) in the ensemble for extratropical seasonal prediction (e.g., Barnett 1995;Kumar and Hoerling 1995). These estimates can vary depending upon the region, strength of the ENSO event, and season being considered. For example the northern Pacific–North America region in winter has shown potential predictability during ENSO years and therefore one might be able to use a smaller sample size in the ensemble. The number of ensemble members in this study was relatively small (five) and not large enough to say definitively whether these extratropical precipitation patterns are indeed associated with the tropical SSTs or in fact internal random variability associated with the coupled system. However, due to the fact that this study is centered on the Pacific–North America region we feel that the limited ensemble size may provide a reasonable estimate of the variability of the coupled model.

6. Regional model results

The past sections have shown that both the global coupled and uncoupled model were able to simulate many of the basic large-scale features associated with the ENSO event of 1987–89. In this section results are presented from the regional model’s seasonal integration. Unless specified otherwise, the results are taken from the ensemble mean.

a. Time series of the area average precipitation differences for the southeast United States

Time series of the area-average, land-only precipitation for the southeast United States for 1987 (1988) minus 1988 (1989) from a member of the ensemble for both the coupled model and its regional model are shown in Fig. 7. The domain for the averaging was 26°–36°N and 265°–285°W. Immediately apparent are the higher rainfall amounts during the warm phase in both the global and regional models. The domain-averaged precipitation differences for the 120-day integrations are +2.46 mm day−1 for the regional model and +1.98 mm day−1 for the global model. The largest difference between the two years occurs in December in both the global and regional models.

The regional model produced the same number of precipitation events as found in the global model. This results from the fact that all but a small percentage of the precipitation was generated by the parameterization of the large-scale rainfall. This is especially true during the winter season in the extratropics. We therefore do not expect the regional model’s precipitation to differ substantially from the global model, since the synoptic-scale waves that drive most of the precipitation are largely influenced by global model. The fact that both the global and regional models produced nearly the same time series highlights the regional model’s ability to consistently maintain the large-scale flow.

b. Spatial patterns

The lowest sigma level average 1200 UTC temperatures for November 1987 from both the regional model and the coupled model are shown in Fig. 8. These results are from a single member of the ensemble. As expected, the regional model with its enhanced resolution was better able to resolve many features not resolved by the global model. The regional model’s coastlines are clearly resolved, as are Cuba, south Florida, and the Yucatan Peninsula. Resolving Cuba and south Florida led to less wavelike temperature patterns east and west of Florida in the regional model. As mentioned earlier the regional models perturbation orography was obtained from a T240 global model dataset, which has a resolution comparable to the regional model’s 40-km resolution. The perturbation orography does add details to the regional model solution over the eastern United States. For example, over western Virginia the global model produced a cold pool (274 K), while the regional model with the perturbation orography shows the 275-K isotherm extending along the Appalachian Mountains through western Virginia and North Carolina. The perturbation orography tended to reduce the penetration of the cold temperatures to the east and south of the mountain chain.

We also note that the models do appear to have a cold bias. Although direct comparisons with ECWMF model sigma surfaces were not done, we believe that our biases are on the order of 3 K based on ECMWF surface and 1000-hPa temperatures and the fact that our lowest sigma surface is located approximately 80 m above the surface. We expect that inclusion of a better land surface parameterization will help in reducing most of the temperature biases, which appears to be emanating from the calculation of the surface temperatures.

Spatially, the monthly precipitation differences for January and February from the coupled and regional models are briefly described. Comparisons are made with the coarse-resolution GPCC analysis and the higher spatial resolution of the U.S. cooperative station data. Figure 9 shows these results for the southeastern United States from the global and regional models along with the corresponding GPCC analysis. Figure 10 shows the corresponding precipitation observations obtained from the National Climatic Data Center archive of U.S. cooperative station data. The station observations were gridded by applying a Cressman analysis to the data. Over the southeastern United States both models simulated the locations of the precipitation differences well during both months. During January, GPCC and the corresponding cooperative station data show the axis of positive amounts oriented from the southwest to northeast extending from the Gulf of Mexico northward along the eastern coast of the United States. The coupled and regional models agree better with the cooperative station data, which extends the +1 mm day−1 precipitation amounts farther northward into Virginia during January.

During February the axis of maximum precipitation is oriented west to east along the Gulf Coast states in both the GPCC and cooperative station data (Figs. 9f and 10b). Both the coupled and regional models were able to simulate these changes in the precipitation orientation between January and February. The magnitude of the model’s precipitation during February agreed well with the coarse GPCC data of 1–2 mm day−1; however, they underestimated the amount by almost a factor of 2 compared to the cooperative station data. As expected, the regional model was not able to improve upon the global precipitation signal in the midwestern United States.

c. Western United States precipitation patterns

The past sections have shown that the global and regional models do produce similar precipitation patterns and magnitudes in regions were the local forcings are not significantly different. This is not the case in the western United States where precipitation is strongly tied to the local orography. To demonstrate that the global and regional model solutions do differ in the presence of orographic forcing we examine the two models over the western United States. The regional model’s orography clearly identifies the coastal range mountains in northern and southern California and the Sierra Nevada range, while the global model failed to distinguish any of these features (Fig. 11). In fact the highest elevation in the Sierra Nevada range in the regional model is 2800 m centered on the California–Nevada border, while the global model only shows a 1400-m contour line running the length of the California–Nevada border.

The precipitation from the first two months of the 1987 boreal winter forecast from the coupled and regional model over California and Nevada are shown in Fig. 12 along with the observed cooperative station values. Both models did well in simulating the increase in the precipitation over California during December. However, because of the global model’s broad and diffuse orography it was unable to properly simulate the magnitude and location of the precipitation along the Sierra Nevada and along the coastal range. For example, during December the global model’s maximum precipitation value was 14 mm day−1 located in the northwest corner of the state with the axis of maximum precipitation extending southward along the western part of the state while the observed shows maximum values of 15 mm day−1 farther east in north-central California along the Sierra Nevada range. In December the regional model shows a maximum value of 16 mm day−1 in north-central California (Fig. 12e) slightly west of the observed with an axis of maximum values extending southward along the Sierra Nevada. A secondary line of maximum values can also be found in the regional model and in the observations extending north along the coast from the San Francisco Bay and southward from Los Angeles. The precipitation along the southern California coast noted in the regional model and found in the observations is completely absent in the global solution in November and marginally represented (1 mm day−1) during December.

The regional model’s better-resolved orographic features allowed it to simulate the magnitude and location of the precipitation along the Sierra Nevada and Coastal Range during November and December better than the global model. However, as seen in December, the regional model has a tendency to overestimate the amount of precipitation over the steep orography of the Sierra Nevada when compared to observations. Part of this might be due to the coarseness of the global model solution entering into the regional domain and part might have to due with the way our model treats orographic lifting and condensation. It is possible that the resolution of the global model might have to be increased to adequately resolve and place important features such as the subtropical and polar jets. We are currently looking into this problem.

d. Downscaling issues

Finally, we say a word about downscaling and the regional model. The basic idea in downscaling is to use output from a model to force a higher-resolution model, such as a crop model. It is known that crop yields over the United States are sensitive to ENSO variations (Adams et al. 1995). However, to adequately use a crop model to forecast yields, higher-order moments of such fields as precipitation and surface maximum and minimum temperatures have to be supplied at the station or county level. In addition to the high spatial resolution, high temporal resolution is also required by the downscaled models. Monthly means alone are generally not sufficient. If the resolution of the parent model is coarse, as it generally is in a climate model, then details can be lost or not even present when downscaling is done. This occurs in both space and time. The regional spectral model allows much higher resolution in both space and time with little extra computing cost. This information is more suitable for use in downscaling models such as crop and river basin models.

To illustrate some of the finer detail provided by the regional model, we show an example from a single day during the integration. Figure 13 shows a member of the ensembles 1200 UTC surface temperature and the daily averaged precipitation from both the coupled and regional model over the southeast United States from day 9 of the 1987 integration. While both models simulated the same basic patterns, the regional model’s surface features are better defined. The low pressure system centered over southern Indiana and its accompanying cold front extending southward into Mississippi and Louisiana are more realistic in the regional model with the tighter packing of the isotherms. Additionally, the regional model was able to resolve the higher elevation of the Appalachian Mountains as evident from the colder surface temperatures along western Virginia and North Carolina. This feature was absent in the global model solution.

The regional model’s precipitation also shows more finescale features when compared to the global model. In contrast to the global model, the regional model simulates two distinct precipitation areas over the southeast United States. The first one is aligned with the cold front and has precipitation extending through Mississippi and Louisiana. The global model was unable to simulate the alignment of the precipitation with the cold front. The second area of precipitation occurs off north Florida, Georgia, and South Carolina. Both global and regional models do produce this feature; however, there are two differences. First the global model axis of maximum amounts is located along the coast of South Carolina and extends south into north Florida, while the regional model axis is farther to the west, closer to the cold front. In the regional model the secondary precipitation is located a few hundred kilometers ahead of the cold front and oriented parallel to the cold front. Although not shown, similar details in the surface temperature and precipitation are also seen in the western United States regional integration. From the view point of downscaling, the added spatial and temporal resolution supplied by the regional model is superior to the global model’s solution.

7. Discussion and conclusions

The initial results of the seasonal predictions presented here are encouraging. The coupled global model reproduces much of the large-scale features associated with ENSO, such as the temperature and precipitation anomalies for 1987–88. In order for the regional model to perform well, it generally must have the best possible lateral boundary conditions. Many studies have shown (see, e.g., Anthes 1983) that the largest source of error in a regional model is error associated with the large scale due to the lateral boundary conditions. For ENSO impact studies, it is imperative that the lateral boundaries, that is, the global model solution, contain the large-scale signatures of the ENSO response. If the global model does not predict the proper ENSO response, it is doubtful that a regional model could do so even if it had ideal physics. In order to achieve a better global model solution, we ran the model at a higher resolution (T63) than is used in almost all other climate models including coupled GCMs. When the improved land surface parameterization scheme is complete, it will be implemented in both the global and regional models, at least to some extent.

The regional model results are very consistent with those of the coupled global model, and in reasonable agreement with the observed. But while the regional model retains the large-scale features of the global model, it provides extra detail, particularly around the coastlines and mountains. The daily precipitation and frontal systems, for example, look more realistic. For the western U.S. run, the monthly precipitation distribution is much closer to the observed station data. The agreement of the regional and global model solutions on the large scale indicates that the large-scale information is effectively transmitted into the regional domain. Since the models use the same physics, and in the southeast United States orographic differences are not a significant factor, we would not expect there to be much drift of the region model climatology from that of the global. Furthermore, in the winter southeast U.S. cases, the predominant weather patterns originate outside the regional domain and thus the regional model climatology is primarily driven by the global model. Thus, when a detailed land surface scheme is implemented, we will have more confidence that, if there is any significant drift in the climatology, it will be due to the improved local forcings and not because of errors associated transmittal of large-scale information through the lateral boundaries. Studies with other regional models indicate that errors due to the latter can be detrimental, particularly with large domains (Jones et al. 1995; Podzun et al. 1995; Waldron et al. 1996). In a study by Ji and Verneker (1997), these kinds of errors were mentioned as a possible cause of drift of precipitation in their model. However, the domain size that we use here is not quite as large as used in Ji and Verneker (1997) or the largest used in Jones et al. (1995), so we cannot make any firm comparisons of the different nesting methods at this time.

It may be tempting to view the regional model result as simply a minor enhancement or embellishment of the global model solution, and that it is not too surprising that the large-scale features agree because the regional model is constrained to do so. We think that this view is not entirely correct. The regional model can develop a solution that is different from the global model on those scales that it can resolve, including the near-synoptic to synoptic scales. We have seen this in numerous hurricane prediction experiments (e.g., Cocke 1998). The size and intensity of simulated hurricanes are strongly dependent on resolution, and in hurricane experiments the perturbations can be quite large. When the regional model predicts a different storm track from the global model, the perturbations can be as large or larger than the regional fields themselves over a significant portion of the regional domain. As another example, in an experiment of the 1987–88 Asian summer monsoon, the regional model was better able to reproduce the interannual variability of precipitation over India due to the model producing more monsoon disturbances that penetrated farther inland in 1988 along the monsoon trough (LaRow and Cocke 1997). As long as the perturbations are not excessively damped or diffused throughout most of the interior, the regional model is capable of producing a different solution from the global as local forcings and resolution permit. The essential feature of the perturbation method is that there is a separation of horizontal scales that allow a more accurate computation of the horizontal derivatives. When the perturbations remain small during the course of integration, it is due to the regional and global models having consistent solutions, not due to a constraint, with the exception of the outermost lateral boundary grid points that are relaxed.

On the whole, the regional model appears to work as designed. It will provide more suitable output for higher-resolution downscaling models, such as crop models, especially when the new land surface scheme is fully implemented and tested.

Acknowledgments

We would like to thank C. E. Williford for providing us with the atmospheric datasets used in these experiments. This work was supported by NOAA Grants NA76GP0521 and NA86GP0031. All experiments were conducted on the SGI Origin 2000 at The Florida State University.

REFERENCES

  • Adams, R. M., K. J. Bryant, B. A. McCarl, D. M. Legler, J. J. O’Brien, A. Solow, and R. Weiher, 1995: The value of improved long-range weather information: Southeastern US ENSO forecasts as they influence US argriculture. Contemp. Econ. Policy,13, 10–13.

  • Anthes, R. A., 1983: Regional models of the atmosphere in the middle latitudes. Mon. Wea. Rev.,111, 1306–1335.

  • ——, 1995: Monte Carlo climate forecasts. J. Climate,8, 1005–1022.

  • ——, M. Latif, E. Kirk, and E. Roeckner, 1991: On ENSO physics. J. Climate,4, 487–515.

  • Brink, D. M., and G. R. Satchler, 1979: Angular Momentum. Oxford University Press, 160 pp.

  • Businger, J. A., J. C. Wyngard, Y. Izumi, and E. F. Bradley, 1971: Flux profile relationship in the atmospheric surface layer. J. Atmos. Sci.,28, 181–189.

  • Chen, Q. S., and Y. H. Kuo, 1992a: A harmonic-sine series expansion and its application to the partitioning and reconstruction problem in a limited area. Mon. Wea. Rev.,120, 91–112.

  • ——, and ——, 1992b: A consistency condition for the wind field reconstruction in a limited area and a harmonic-cosine series expansion. Mon. Wea. Rev.,120, 2653–2670.

  • ——, L.-S. Bai, and D. H. Bromwich, 1997: A harmonic-Fourier spectral limited-area model with an external wind lateral boundary condition. Mon. Wea. Rev.,125, 143–167.

  • Cocke, S., 1998: Case study of Erin using the FSU Nested Regional Spectral Model. Mon. Wea. Rev.,126, 1337–1346.

  • Dickinson, R. E., R. M. Errico, F. Giorgi, and G. T. Bates, 1989: A regional climate model for the western United States. Climatic Change,15, 383–422.

  • ——, A. Henderson-Sellers, and P. J. Kennedy, 1993: Biosphere–Atmosphere Transfer Scheme (BATS) version 1E as coupled to the NCAR Community Climate Model. NCAR Tech. Note TN387+STR, 72 pp.

  • Fulton, S. R., and W. H. Schubert, 1987a: Chebyshev spectral methods for limited-area models. Part I: Model problem analysis. Mon. Wea. Rev.,115, 1940–1953.

  • ——, and ——, 1987b: Chebyshev spectral methods for limited-area models. Part II: Shallow water model. Mon. Wea. Rev.,115, 1954–1965.

  • Giorgi, F., 1995: Perspectives for regional earth system modeling. Global Planet. Change,10, 23–42.

  • Harshvardan, and T. G. Corsetti, 1984: Long-wave parameterization for the UCLA/GLAS GCM. NASA Tech. Memo. 86072, 52 pp. [Available from Goddard Space Flight Center, Greenbelt, MD 20771.].

  • Haugen, J. E., and B. Machenhauer, 1993: A spectral limited-area model formulation with time-dependent boundary conditions applied to the shallow water equations. Mon. Wea. Rev.,121, 2618–2630.

  • Hoyer, J. M., 1987: The ECMWF spectral limited-area model. Workshop Proc. on Techniques for Horizontal Discretization in Numerical Weather Prediction Models, Shinfield Park, Reading, United Kingdom, ECMWF, 343–359.

  • Huffman, G. J., and Coauthors, 1997: The Global Precipitation Climatology Project (GPCP) combined precipitation dataset. Bull. Amer. Meteor. Soc.,78, 5–20.

  • Janowick, S. E., and P. A. Arkin, 1991: Rainfall variations in the tropics during 1986–1989, as estimated from observations of cloud-top temperatures. J. Geophys. Res.,96, 3359–3373.

  • Ji, Y., and A. D. Vernekar, 1997: Simulation of the Asian summer monsoons of 1987 and 1988 with a regional model nested in a global GCM. J. Climate,10, 1965–1979.

  • Jones, R. G., J. M. Murphy, and M. Noguer, 1995: Simulation of climate change over Europe using a nested regional climate model. I: Assessment of control climate, including sensitivity to location of lateral boundaries. Quart. J. Roy. Meteor. Soc.,121, 1413–1449.

  • Juang, H.-M. H., and M. Kanamitsu, 1994: The NMC Nested Regional Spectral Model. Mon. Wea. Rev.,122, 3–26.

  • Kanamitsu, M., 1975: On numerical prediction over a global tropical belt. Dept. of Meteorology, Rep. 75-1, The Florida State University, 282 pp. [Available from Dept. of Meteorology, Florida State University, Tallahassee, FL 32306.].

  • ——, K. Tada, K. Kudo, N. Sato, and S. Isa, 1983: Description of the JMA operational spectral model. J. Meteor. Soc. Japan,61, 812–828.

  • Kida, H., T. Koide, H. Sasaki, and M. Chiba, 1991: A new approach to coupling a limited area model with a GCM for regional climate simulation. J. Meteor. Soc. Japan,69, 723–728.

  • Kitade, T., 1983: Nonlinear normal mode initialization with physics. Mon. Wea. Rev.,111, 2194–2213.

  • Krishnamurti, T. N., S. Low-Nam, and R. Pasch, 1983: Cumulus parameterization and rainfall rates II. Mon. Wea. Rev.,111, 816–828.

  • ——, J. Xue, H. S. Bedi, K. Ingles, and D. Oosterhof, 1991: Physical initialization for numerical weather prediction over the tropics. Tellus,43AB, 53–81.

  • ——, H. S. Bedi, and V. M. Hardiker, 1998: An Introduction to Global Spectral Modeling. Oxford University Press, 252 pp.

  • Kumar, A., and M. P. Hoerling, 1995: Prospects and limitations of seasonal atmospheric GCM predictions. Bull. Amer. Meteor. Soc.,76, 335–345.

  • ——, and ——, 1997: Interpretation and limitations of the observed inter–El Niño variability. J. Climate,10, 83–91.

  • Lacis, A. A., and J. E. Hansen, 1974: A parameterization of the absorption of solar radiation in the earth’s atmosphere. J. Atmos. Sci.,31, 118–133.

  • LaRow, T. E., and S. Cocke, 1997: Asian monsoon seasonal simulations using a nested regional model embedded in a coupled ocean-atmosphere model. Proc. 22d Annual Climate Diagnostics and Prediction Workshop, Berkeley, CA, Amer. Meteor. Soc., 334–336.

  • ——, and T. N. Krishnamurti, 1998: Initial conditions and ENSO prediction using a coupled ocean–atmosphere model. Tellus,50A, 76–94.

  • Latif, M., 1987: Tropical ocean circulation experiments. J. Phys. Oceanogr.,17, 246–263.

  • ——, A. Sterl, E. Maier-Reimer, and M. M. Junge, 1993: Structure and predictability of the El Niño–Southern Oscillation phenomenon in a coupled–ocean atmosphere general circulation model. J. Climate,6, 700–709.

  • ——, T. P. Barnett, M. A. Cane, M. Flugel, N. E. Graham, H. von Storch, J. S. Xu, and S. E. Zebiak, 1994: A review of ENSO prediction studies. Climate Dyn.,9, 167–179.

  • Louis, J. F., 1979: A parametric model of vertical eddy fluxes in the atmosphere. Bound.-Layer Meteor.,17, 187–202.

  • McGregor, J. L., 1997: Regional climate modelling. Meteor. Atmos. Phys.,63, 105–117.

  • ——, K. J. Walsh, and J. J. Katzfey, 1993: Nested modelling for regional climate studies. Modelling Change in Environmental Systems, A. J. Jakeman et al., Eds., John Wiley, 367–386.

  • Pan, H.-L., and W. S. Wu, 1994: Implementing a mass flux convection parameterization package for the NMC MRF model. Preprints, Tenth Conf. on Numerical Weather Prediction, Portland, OR, Amer. Meteor. Soc., 96–98.

  • Podzun, R., A. Cress, D. Majewski, and V. Renner, 1995: Simulation of European climate with a limited area model. Part II. AGCM boundary conditions. Contrib. Atmos. Phys.,68, 205–225.

  • Reynolds, R. W., 1988: A real-time global sea surface temperature analysis. J. Climate,1, 75–86.

  • Stricherz, J. N., J. J. O’Brien, and D. M. Legler 1992: Atlas of Florida State University: Tropical Pacific Winds for TOGA 1966–1985. The Florida State University, 275 pp.

  • Tatsumi, Y., 1986: A spectral limited-area model with time dependent lateral boundary conditions and its application to a multi-level primitive equation model. J. Meteor. Soc. Japan,64, 637–663.

  • Tiedke, M., 1984: The sensitivity of the time-mean large-scale flow to cumulus convection in the ECMWF model. Workshop on Convection in Large-Scale Numerical Models, Shinfield Park, Reading, United Kingdom, ECMWF, 297–316.

  • Waldron, K., J. Paegle, and J. D. Horel, 1996: Sensitivity of a spectrally filtered and nudged limited-area model to outer model options. Mon. Wea. Rev.,124, 529–547.

  • Wallace, J. M., S. Tibaldi, and A. J. Simmons, 1983: Reduction of systematic forecast errors in the ECMWF model through the introduction of envelope orography. Quart. J. Roy. Meteor. Soc.,109, 683–718.

APPENDIX A

Derivation of the Model Equations

Both the regional and global models use the same vertical σ coordinate, where σ is P/Ps. Following Krishnamurti et al. (1998), the hydrostatic primitive equations in spherical coordinates can be written as follows: divergence equation,
i1520-0493-128-3-689-ea1
vorticity equation,
i1520-0493-128-3-689-ea2
thermodynamics equation,
i1520-0493-128-3-689-ea3
continuity equation,
i1520-0493-128-3-689-ea4
moisture equation,
i1520-0493-128-3-689-ea5
where
i1520-0493-128-3-689-ea6
and T∗ = 300 K for all levels, with R the gas constant;T the virtual temperature; q the log of the surface pressure; a the earth radius; D, ζ the divergence and vorticity; u, υ the wind components scaled by cos(θ)/a, and S the moisture variable (specific humidity). For the regional model in the Mercator projection, we define a modified Laplacian, divergence, and vorticity according to
i1520-0493-128-3-689-ea21
where mF = cos−2θ is the map factor. The modified divergence and vorticity, D̃, ζ̃, are related to the wind components by
i1520-0493-128-3-689-ea24
and are convenient for conversion to and from the wind components in spectral space where the perturbation variables are represented by trigonometric functions. The modified Laplacian is ;tz∇2 = ∂2/∂x2 + ∂2/∂y2 and has trigonometric eigenfunctions. The primitive equations can now be written as follows:
i1520-0493-128-3-689-ea26
where RHSD, RHSζ, RHSP, RHSq, and RHSS are the right-hand sides of the primitive equations (A1)–(A5), respectively. The presence of the map factor means that in order to separate the linear and nonlinear terms, we must linearize the equations with respect to mF via mFm0 + m′, m0 constant. Generally, m0 is taken to be the domain average of mF, though for stability reasons a larger value may be used. Using a leapfrog, semi-implicit time integration scheme the finite difference (in time) form of the equations become
i1520-0493-128-3-689-ea31
where
i1520-0493-128-3-689-ea36

The operators A, I are the second-order vertical finite differencing operator and vertical finite integration operator, respectively, and are identical to those used in FSUGSM.

We have thus separated the nonlinear terms (which are computed in grid space) on the right-hand side and the linear terms on the left-hand side. We may split the regional variables into a sum of perturbation plus base (global), and we obtain the equations for the perturbations
i1520-0493-128-3-689-ea38
All of the terms on the right-hand side are computed on the transform grid. The above equations are Fourier analyzed using double trigonometric cosine series (or sine in the case of the vorticity equation). The Laplacian becomes {;tz∇2}mn = −a−2[(mfx)2 + (nfy)2], where fx, fy are scale factors equal to π/(angular extension of the domain). The equations in spectral space are
i1520-0493-128-3-689-ea43
where RHSD′, RHSP′, RHSζ′, RHSq′, and RHSS′ are the right-hand sides of the perturbation equations (A38)–(A42), respectively. Using the definition of the time differencing and time-averaging operators, (A36) and (A37), (A43) and (A45) can be combined to solve for Pmn(t + Δt). This is a linear tridiagonal system of equations in the vertical to be solved for each mode (m, n). The system is tridiagonal due to the second-order differencing operator A, and fast algorithms exist to solve it. The other perturbations at time t + Δt are then easily solved. This procedure is exactly the same as in the global model, so we do not repeat the details here (see Krishnamurti et al. 1998).

APPENDIX B

FSU Global Spectral Model

Table B1. Outline of the FSU Global Spectral Model.

i1520-0493-128-3-689-t201

Fig. 1.
Fig. 1.

Regional model domains.

Citation: Monthly Weather Review 128, 3; 10.1175/1520-0493(2000)128<0689:SPUARS>2.0.CO;2

Fig. 2.
Fig. 2.

Nov–Jan average Pacific sea surface temperature differences from (a) coupled model and (b) ECMWF. Contour interval is 1 K.

Citation: Monthly Weather Review 128, 3; 10.1175/1520-0493(2000)128<0689:SPUARS>2.0.CO;2

Fig. 3.
Fig. 3.

Northern Hemisphere 1988 minus 1989 January 500-hPa heights from (a) control, (b) coupled model, and (c) ECMWF. Contour interval is 50 m; ±25 m contours shown in (a) and (c) for clarity.

Citation: Monthly Weather Review 128, 3; 10.1175/1520-0493(2000)128<0689:SPUARS>2.0.CO;2

Fig. 4.
Fig. 4.

Northern Hemisphere 1988 minus 1989 January 850-hPa temperature from (a) control, (b) coupled model, and (c) ECMWF. Contour interval is 2°.

Citation: Monthly Weather Review 128, 3; 10.1175/1520-0493(2000)128<0689:SPUARS>2.0.CO;2

Fig. 5.
Fig. 5.

The 1987 minus 1988 Nov precipitation from the coupled model, the control, and GPCC. Contour values are +10 and −10 mm month−1. Shaded values greater than 10 mm month−1 for clarity.

Citation: Monthly Weather Review 128, 3; 10.1175/1520-0493(2000)128<0689:SPUARS>2.0.CO;2

Fig. 6.
Fig. 6.

The 1988 minus 1989 January precipitation from the coupled model, the control, and GPCC. Contour values are +10 and −10 mm month−1. Shaded values greater than 10 mm month−1 for clarity.

Citation: Monthly Weather Review 128, 3; 10.1175/1520-0493(2000)128<0689:SPUARS>2.0.CO;2

Fig. 7.
Fig. 7.

Time series for the area average, land-only precipitation differences for Nov–Feb 1987 (1988) minus 1988 (1989) for the coupled and regional model. Contour interval is 1 mm day−1.

Citation: Monthly Weather Review 128, 3; 10.1175/1520-0493(2000)128<0689:SPUARS>2.0.CO;2

Fig. 8.
Fig. 8.

The November 1987 lowest sigma model level average temperature for (top) regional model and (bottom) global model. Contour interval is 1 K.

Citation: Monthly Weather Review 128, 3; 10.1175/1520-0493(2000)128<0689:SPUARS>2.0.CO;2

Fig. 9.
Fig. 9.

The 1988 minus 1989 Jan and Feb precipitation for the southeast United States: (a) Jan global model, (b) Jan regional model, (c) Jan GPCC, (d) Feb global model, (e) Feb regional model, and (f) Feb GPCC. Contour interval is 1 mm day−1. Positive values shaded greater than 1 mm day−1.

Citation: Monthly Weather Review 128, 3; 10.1175/1520-0493(2000)128<0689:SPUARS>2.0.CO;2

Fig. 10.
Fig. 10.

The 1988 minus 1989 cooperative station precipitation differences for the southeast United States: (a) Jan and (b) Feb. Contour interval is 1 mm day−1. Positive values shaded greater than 1 mm day−1.

Citation: Monthly Weather Review 128, 3; 10.1175/1520-0493(2000)128<0689:SPUARS>2.0.CO;2

Fig. 11.
Fig. 11.

Orography of the western United States: (a) regional model and (b) global model. Contour interval is 200 m starting at 400 m.

Citation: Monthly Weather Review 128, 3; 10.1175/1520-0493(2000)128<0689:SPUARS>2.0.CO;2

Fig. 12.
Fig. 12.

The 1987 Nov and Dec precipitation for the western United States: (a) Nov global model, (b) Nov regional model, (c) Nov observed cooperative station data, (d) Dec global model, (e) Dec regional model, and (f) Dec observed cooperative station data. Contour interval is 1 mm day−1.

Citation: Monthly Weather Review 128, 3; 10.1175/1520-0493(2000)128<0689:SPUARS>2.0.CO;2

Fig. 13.
Fig. 13.

The 9 Nov 1987 output for the southeast United States: (a) 1200 UTC global model’s surface temperature, (b) 1200 UTC regional model’s surface temperature, (c) accumulated precipitation for day 9 from the global model, and (d) accumulated precipitation for day 9 from the regional model. Contour intervals are 1 K and 3 mm day−1.

Citation: Monthly Weather Review 128, 3; 10.1175/1520-0493(2000)128<0689:SPUARS>2.0.CO;2

Save
  • Adams, R. M., K. J. Bryant, B. A. McCarl, D. M. Legler, J. J. O’Brien, A. Solow, and R. Weiher, 1995: The value of improved long-range weather information: Southeastern US ENSO forecasts as they influence US argriculture. Contemp. Econ. Policy,13, 10–13.

  • Anthes, R. A., 1983: Regional models of the atmosphere in the middle latitudes. Mon. Wea. Rev.,111, 1306–1335.

  • ——, 1995: Monte Carlo climate forecasts. J. Climate,8, 1005–1022.

  • ——, M. Latif, E. Kirk, and E. Roeckner, 1991: On ENSO physics. J. Climate,4, 487–515.

  • Brink, D. M., and G. R. Satchler, 1979: Angular Momentum. Oxford University Press, 160 pp.

  • Businger, J. A., J. C. Wyngard, Y. Izumi, and E. F. Bradley, 1971: Flux profile relationship in the atmospheric surface layer. J. Atmos. Sci.,28, 181–189.

  • Chen, Q. S., and Y. H. Kuo, 1992a: A harmonic-sine series expansion and its application to the partitioning and reconstruction problem in a limited area. Mon. Wea. Rev.,120, 91–112.

  • ——, and ——, 1992b: A consistency condition for the wind field reconstruction in a limited area and a harmonic-cosine series expansion. Mon. Wea. Rev.,120, 2653–2670.

  • ——, L.-S. Bai, and D. H. Bromwich, 1997: A harmonic-Fourier spectral limited-area model with an external wind lateral boundary condition. Mon. Wea. Rev.,125, 143–167.

  • Cocke, S., 1998: Case study of Erin using the FSU Nested Regional Spectral Model. Mon. Wea. Rev.,126, 1337–1346.

  • Dickinson, R. E., R. M. Errico, F. Giorgi, and G. T. Bates, 1989: A regional climate model for the western United States. Climatic Change,15, 383–422.

  • ——, A. Henderson-Sellers, and P. J. Kennedy, 1993: Biosphere–Atmosphere Transfer Scheme (BATS) version 1E as coupled to the NCAR Community Climate Model. NCAR Tech. Note TN387+STR, 72 pp.

  • Fulton, S. R., and W. H. Schubert, 1987a: Chebyshev spectral methods for limited-area models. Part I: Model problem analysis. Mon. Wea. Rev.,115, 1940–1953.

  • ——, and ——, 1987b: Chebyshev spectral methods for limited-area models. Part II: Shallow water model. Mon. Wea. Rev.,115, 1954–1965.

  • Giorgi, F., 1995: Perspectives for regional earth system modeling. Global Planet. Change,10, 23–42.

  • Harshvardan, and T. G. Corsetti, 1984: Long-wave parameterization for the UCLA/GLAS GCM. NASA Tech. Memo. 86072, 52 pp. [Available from Goddard Space Flight Center, Greenbelt, MD 20771.].

  • Haugen, J. E., and B. Machenhauer, 1993: A spectral limited-area model formulation with time-dependent boundary conditions applied to the shallow water equations. Mon. Wea. Rev.,121, 2618–2630.

  • Hoyer, J. M., 1987: The ECMWF spectral limited-area model. Workshop Proc. on Techniques for Horizontal Discretization in Numerical Weather Prediction Models, Shinfield Park, Reading, United Kingdom, ECMWF, 343–359.

  • Huffman, G. J., and Coauthors, 1997: The Global Precipitation Climatology Project (GPCP) combined precipitation dataset. Bull. Amer. Meteor. Soc.,78, 5–20.

  • Janowick, S. E., and P. A. Arkin, 1991: Rainfall variations in the tropics during 1986–1989, as estimated from observations of cloud-top temperatures. J. Geophys. Res.,96, 3359–3373.

  • Ji, Y., and A. D. Vernekar, 1997: Simulation of the Asian summer monsoons of 1987 and 1988 with a regional model nested in a global GCM. J. Climate,10, 1965–1979.

  • Jones, R. G., J. M. Murphy, and M. Noguer, 1995: Simulation of climate change over Europe using a nested regional climate model. I: Assessment of control climate, including sensitivity to location of lateral boundaries. Quart. J. Roy. Meteor. Soc.,121, 1413–1449.

  • Juang, H.-M. H., and M. Kanamitsu, 1994: The NMC Nested Regional Spectral Model. Mon. Wea. Rev.,122, 3–26.

  • Kanamitsu, M., 1975: On numerical prediction over a global tropical belt. Dept. of Meteorology, Rep. 75-1, The Florida State University, 282 pp. [Available from Dept. of Meteorology, Florida State University, Tallahassee, FL 32306.].

  • ——, K. Tada, K. Kudo, N. Sato, and S. Isa, 1983: Description of the JMA operational spectral model. J. Meteor. Soc. Japan,61, 812–828.

  • Kida, H., T. Koide, H. Sasaki, and M. Chiba, 1991: A new approach to coupling a limited area model with a GCM for regional climate simulation. J. Meteor. Soc. Japan,69, 723–728.

  • Kitade, T., 1983: Nonlinear normal mode initialization with physics. Mon. Wea. Rev.,111, 2194–2213.

  • Krishnamurti, T. N., S. Low-Nam, and R. Pasch, 1983: Cumulus parameterization and rainfall rates II. Mon. Wea. Rev.,111, 816–828.

  • ——, J. Xue, H. S. Bedi, K. Ingles, and D. Oosterhof, 1991: Physical initialization for numerical weather prediction over the tropics. Tellus,43AB, 53–81.

  • ——, H. S. Bedi, and V. M. Hardiker, 1998: An Introduction to Global Spectral Modeling. Oxford University Press, 252 pp.

  • Kumar, A., and M. P. Hoerling, 1995: Prospects and limitations of seasonal atmospheric GCM predictions. Bull. Amer. Meteor. Soc.,76, 335–345.

  • ——, and ——, 1997: Interpretation and limitations of the observed inter–El Niño variability. J. Climate,10, 83–91.

  • Lacis, A. A., and J. E. Hansen, 1974: A parameterization of the absorption of solar radiation in the earth’s atmosphere. J. Atmos. Sci.,31, 118–133.

  • LaRow, T. E., and S. Cocke, 1997: Asian monsoon seasonal simulations using a nested regional model embedded in a coupled ocean-atmosphere model. Proc. 22d Annual Climate Diagnostics and Prediction Workshop, Berkeley, CA, Amer. Meteor. Soc., 334–336.

  • ——, and T. N. Krishnamurti, 1998: Initial conditions and ENSO prediction using a coupled ocean–atmosphere model. Tellus,50A, 76–94.

  • Latif, M., 1987: Tropical ocean circulation experiments. J. Phys. Oceanogr.,17, 246–263.

  • ——, A. Sterl, E. Maier-Reimer, and M. M. Junge, 1993: Structure and predictability of the El Niño–Southern Oscillation phenomenon in a coupled–ocean atmosphere general circulation model. J. Climate,6, 700–709.

  • ——, T. P. Barnett, M. A. Cane, M. Flugel, N. E. Graham, H. von Storch, J. S. Xu, and S. E. Zebiak, 1994: A review of ENSO prediction studies. Climate Dyn.,9, 167–179.

  • Louis, J. F., 1979: A parametric model of vertical eddy fluxes in the atmosphere. Bound.-Layer Meteor.,17, 187–202.

  • McGregor, J. L., 1997: Regional climate modelling. Meteor. Atmos. Phys.,63, 105–117.

  • ——, K. J. Walsh, and J. J. Katzfey, 1993: Nested modelling for regional climate studies. Modelling Change in Environmental Systems, A. J. Jakeman et al., Eds., John Wiley, 367–386.

  • Pan, H.-L., and W. S. Wu, 1994: Implementing a mass flux convection parameterization package for the NMC MRF model. Preprints, Tenth Conf. on Numerical Weather Prediction, Portland, OR, Amer. Meteor. Soc., 96–98.

  • Podzun, R., A. Cress, D. Majewski, and V. Renner, 1995: Simulation of European climate with a limited area model. Part II. AGCM boundary conditions. Contrib. Atmos. Phys.,68, 205–225.

  • Reynolds, R. W., 1988: A real-time global sea surface temperature analysis. J. Climate,1, 75–86.

  • Stricherz, J. N., J. J. O’Brien, and D. M. Legler 1992: Atlas of Florida State University: Tropical Pacific Winds for TOGA 1966–1985. The Florida State University, 275 pp.

  • Tatsumi, Y., 1986: A spectral limited-area model with time dependent lateral boundary conditions and its application to a multi-level primitive equation model. J. Meteor. Soc. Japan,64, 637–663.

  • Tiedke, M., 1984: The sensitivity of the time-mean large-scale flow to cumulus convection in the ECMWF model. Workshop on Convection in Large-Scale Numerical Models, Shinfield Park, Reading, United Kingdom, ECMWF, 297–316.

  • Waldron, K., J. Paegle, and J. D. Horel, 1996: Sensitivity of a spectrally filtered and nudged limited-area model to outer model options. Mon. Wea. Rev.,124, 529–547.

  • Wallace, J. M., S. Tibaldi, and A. J. Simmons, 1983: Reduction of systematic forecast errors in the ECMWF model through the introduction of envelope orography. Quart. J. Roy. Meteor. Soc.,109, 683–718.

  • Fig. 1.

    Regional model domains.

  • Fig. 2.

    Nov–Jan average Pacific sea surface temperature differences from (a) coupled model and (b) ECMWF. Contour interval is 1 K.

  • Fig. 3.

    Northern Hemisphere 1988 minus 1989 January 500-hPa heights from (a) control, (b) coupled model, and (c) ECMWF. Contour interval is 50 m; ±25 m contours shown in (a) and (c) for clarity.

  • Fig. 4.

    Northern Hemisphere 1988 minus 1989 January 850-hPa temperature from (a) control, (b) coupled model, and (c) ECMWF. Contour interval is 2°.

  • Fig. 5.

    The 1987 minus 1988 Nov precipitation from the coupled model, the control, and GPCC. Contour values are +10 and −10 mm month−1. Shaded values greater than 10 mm month−1 for clarity.

  • Fig. 6.

    The 1988 minus 1989 January precipitation from the coupled model, the control, and GPCC. Contour values are +10 and −10 mm month−1. Shaded values greater than 10 mm month−1 for clarity.

  • Fig. 7.

    Time series for the area average, land-only precipitation differences for Nov–Feb 1987 (1988) minus 1988 (1989) for the coupled and regional model. Contour interval is 1 mm day−1.

  • Fig. 8.

    The November 1987 lowest sigma model level average temperature for (top) regional model and (bottom) global model. Contour interval is 1 K.

  • Fig. 9.

    The 1988 minus 1989 Jan and Feb precipitation for the southeast United States: (a) Jan global model, (b) Jan regional model, (c) Jan GPCC, (d) Feb global model, (e) Feb regional model, and (f) Feb GPCC. Contour interval is 1 mm day−1. Positive values shaded greater than 1 mm day−1.

  • Fig. 10.

    The 1988 minus 1989 cooperative station precipitation differences for the southeast United States: (a) Jan and (b) Feb. Contour interval is 1 mm day−1. Positive values shaded greater than 1 mm day−1.

  • Fig. 11.

    Orography of the western United States: (a) regional model and (b) global model. Contour interval is 200 m starting at 400 m.

  • Fig. 12.

    The 1987 Nov and Dec precipitation for the western United States: (a) Nov global model, (b) Nov regional model, (c) Nov observed cooperative station data, (d) Dec global model, (e) Dec regional model, and (f) Dec observed cooperative station data. Contour interval is 1 mm day−1.

  • Fig. 13.

    The 9 Nov 1987 output for the southeast United States: (a) 1200 UTC global model’s surface temperature, (b) 1200 UTC regional model’s surface temperature, (c) accumulated precipitation for day 9 from the global model, and (d) accumulated precipitation for day 9 from the regional model. Contour intervals are 1 K and 3 mm day−1.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 367 63 12
PDF Downloads 117 29 5