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  • View in gallery

    Schematic representation of the incremental correlation method for a single ensemble member toward the ensemble mean field. The horizontal and vertical axes indicate the time and the value of the atmospheric parameter (wind speed, temperature, etc.), respectively. The black and red thick lines represent the state before and after the incremental correction, respectively. The increment (gray-shaded area) was calculated by differencing the monthly running mean of the ensemble mean and a single member . The increment was then added to the single member.

  • View in gallery

    Climatological seasonal mean precipitation from the EM run: (a)–(c) the results for the boreal winter (DJF) and (d)–(f) the same but for the boreal summer (JJA). Results for the (a),(d) early period (1871–73); (b),(e) recent period (1981–83); and (c),(f) differences between the recent and early periods. The global averaged value (glbave) is shown at the top of each panel.

  • View in gallery

    Seasonal (DJF) mean of moisture divergence in the EM run: (a),(d) the total divergence, (b),(e) the part derived from long-term averages, and (c),(f) the part derived from the transient terms; (a)–(c) shows the earlier period (1871–73) and (d)–(f) the recent period (1981–83).

  • View in gallery

    As in Fig. 2, but for the ICS run.

  • View in gallery

    As in Fig. 3, but for the ICS run.

  • View in gallery

    Spatially averaged RMSD in 500Z against the original 20CR ensemble mean. The EM, ICS, S1, S3, S6, and ICS2 runs are shown as black open circles, green closed circles, blue open squares with error bars, red closed squares, pink crosses, and violet open circles, respectively. S1 has the error bars because there were six patterns in the S1 experiment. Results are shown for (a)–(c) the early period (1871–73) and (d)–(f) the recent period (1981–83). (a),(d) The global-averaged RMSDs, and the (b),(e) Northern Hemisphere and (c),(f) Southern Hemisphere averages. The temporal mean values of each run are shown in parentheses in the legend of symbols.

  • View in gallery

    As in Fig. 6, but for precipitation.

  • View in gallery

    Global mean precipitation by each experiment from 1871 to 2008. The 20CR simulation (green), the EM run (black), and the ICS run (blue) are shown for the entire period. Those runs with the direct use of single members (six S1s) are shown only for 1871–73 and 1981–83 with gray lines.

  • View in gallery

    Vertical profiles of the global averaged absolute increment by ICS during Januaries of 1871 (black lines) and 1981 (green lines) for (a) zonal wind speed, (b) air temperature, and (c) specific humidity.

  • View in gallery

    Global-averaged absolute R term in NLBE in the original single member (Org), the modified single member by ICS (ICS), and the ensemble mean (EM) for January (a) 1871 and (b) 1981.

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Incremental Correction for the Dynamical Downscaling of Ensemble Mean Atmospheric Fields

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  • 1 Atmosphere and Ocean Research Institute, and Institute of Industrial Science, University of Tokyo, Tokyo, Japan
  • | 2 Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California
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Abstract

This research was motivated by the need for an improved method compared to the conventional brute-force approach to ensemble downscaling. That method simply applies dynamical downscaling to each ensemble member. It obtains a reliable forecast by taking the ensemble average of all the downscaled ensemble members. This approach, although straightforward, has a problem in that the computational cost is too large for an operational environment. Herein a method for downscaling ensemble mean forecasts is proposed. Although this method does not provide probabilistic forecasts, it will provide the regional-scale detail at minimum cost. In this product, all of the predicted parameters are dynamically and physically consistent (i.e., most likely to occur on a seasonal time scale). It is believed that such a product has great utility for regional climate forecast and application products. The method applies a correction to one of the global forecast members in such a way that the seasonal mean is equal to that of the ensemble mean, and it then downscales the corrected global forecast. This method was tested for a 140-yr period by using the Twentieth-Century Reanalysis dataset, which is a product of ensemble Kalman filtering data assimilation. Use of the method clearly improves the downscaling skill compared to the case of using only a single member; the skill becomes equivalent to that achieved when between two and six members are used directly.

Deceased.

Corresponding author address: Kei Yoshimura, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8568, Japan. E-mail: kei@aori.u-tokyo.ac.jp

Abstract

This research was motivated by the need for an improved method compared to the conventional brute-force approach to ensemble downscaling. That method simply applies dynamical downscaling to each ensemble member. It obtains a reliable forecast by taking the ensemble average of all the downscaled ensemble members. This approach, although straightforward, has a problem in that the computational cost is too large for an operational environment. Herein a method for downscaling ensemble mean forecasts is proposed. Although this method does not provide probabilistic forecasts, it will provide the regional-scale detail at minimum cost. In this product, all of the predicted parameters are dynamically and physically consistent (i.e., most likely to occur on a seasonal time scale). It is believed that such a product has great utility for regional climate forecast and application products. The method applies a correction to one of the global forecast members in such a way that the seasonal mean is equal to that of the ensemble mean, and it then downscales the corrected global forecast. This method was tested for a 140-yr period by using the Twentieth-Century Reanalysis dataset, which is a product of ensemble Kalman filtering data assimilation. Use of the method clearly improves the downscaling skill compared to the case of using only a single member; the skill becomes equivalent to that achieved when between two and six members are used directly.

Deceased.

Corresponding author address: Kei Yoshimura, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8568, Japan. E-mail: kei@aori.u-tokyo.ac.jp

1. Introduction

Ensemble methods are popularly utilized in global and regional seasonal forecasting, future climate projections, and data assimilation. On a seasonal time scale, the ensemble method explicitly simulates so-called meteorological noise, which is originally defined as the small-scale, high-frequency component of the atmospheric field. Although the word “noise” suggests something nonessential, noise plays an important role in maintaining global general circulation and in generating seasonal mean anomalies. In the final product, the noise is eliminated by taking the ensemble average, which produces the most highly skilled forecast, often exceeding the skill of any of the ensemble members (Kalnay 2003). The ensemble method is also able to provide probabilistic forecasts, essential for the seasonal time range, when the skill is low compared with short- to medium-range predictions.

In data assimilation, similar to the case for ensemble seasonal forecasts, the ensemble method directly yields a global analysis with high frequency (typically every 6 h) as the most likely state of the atmosphere and also yields an uncertainty estimate for that analysis (Compo et al. 2011). By using this technique, Whitaker et al. (2009) showed that the late-nineteenth-century observation network for surface pressure would provide comparable analysis skill for the 500-hPa height, as would a 3-day forecast with the current network.

Ensemble seasonal forecasting or ensemble data assimilation is performed using a global model with relatively low spatial resolution because of the significant computer resource requirement. The most commonly used resolution is about 200–100 km. However, this resolution is too coarse for practical applications, such as hydrological forecasts, crop forecasts, forest fire forecasts, and wind forecasts for wind energy. To overcome this resolution problem, the application of dynamical downscaling has been proposed and intensely investigated. Dynamical downscaling cannot only meet the needs of the finer features of the meteorological parameters but can also produce other side parameters that have not been included in coarse global models. Such parameters include chemical constituents such as aerosols (Grell et al. 2005), greenhouse gases (Beck et al. 2011), isotopes (Yoshimura et al. 2010), groundwater interaction (Jiang et al. 2009), dynamic vegetation (Niu et al. 2011), sediment transport (Warner et al. 2008), and so forth. In other words, dynamical downscaling is a technique for diagnosing the physically consistent meteorological fields and relevant derivative parameters with a coarse atmospheric forcing (Kanamitsu et al. 2010).

Lately, the dynamical downscaling of coarse ensemble data has been in increasing demand. To date, most such studies have simply downscaled some or all of the global ensemble members and computed the ensemble mean to obtain the most likely forecast or analysis at the regional scale. This simple method, however, has the problem of computational cost, which can be prohibitive in an operational environment. The resolution of global models has been improving steadily, and a resolution of 50 km, commonly used in regional downscaling 2–3 yr ago, is common in global models today. An acceptable resolution ratio between a coarse-resolution global model and a fine-resolution regional model is from about 10 to 20. Note that we often use the multiple-nesting method (e.g., from global 200-km resolution, 50-km resolution for the first domain and 10-km resolution for the second domain). In this case, additional computational cost is necessary for the intermediate domain(s) (in this example, the 50-km resolution domain). The size of the domain varies significantly depending on the purpose, but in the case of the contiguous United States, the final domain is approximately (assuming a 50° latitude × 60° longitude area) of the globe. Because computation time is inversely proportional to the third power of the grid size (if the same vertical resolution is used), this regional model requires 50 (i.e., 103/20) to 400 (i.e., 203/20) times more computer resources than does a global model. Even if a time-slice method is used to limit the regional model-integration period, the required computer resources are still 10–80 times greater than for the original coarse runs.

Thus, from an economic point of view, it would be beneficial if a single downscaled forecast corresponding to the best-estimate ensemble mean could be produced with a single downscaling run, so that one is able to afford a higher resolution instead of running a large number of ensemble members. Therefore, we will suggest in this study a new, economical method for realizing such a run, that is, dynamical downscaling of the ensemble mean atmospheric field. This downscaling run cannot provide probabilistic information as it is applied, but it is probably impractical to expect probabilistic information from regional ensemble downscaling in an operational environment because of its high computational cost.

This effort will help solve a general problem of ensemble forecasting: inconsistency between dynamical and physical fields. In ensemble mean fields, the well-known synoptic relations between large-scale patterns, and precipitation and near-surface temperature, may be lacking (e.g., Alexandru et al. 2007; Lucas-Picher et al. 2008). As a very simple example, it is possible that a large amount of precipitation can be forecasted in the middle of a high pressure system in the ensemble mean when one anomalous member predicts a low pressure system with significant precipitation, while all other members predict a high pressure system without precipitation. Very similar situations can arise easily for relations among temperature, precipitation, cloudiness, and other parameters. It would be most useful for forecasters if we could provide forecasts of all the variables that were dynamically and physically consistent with one another and hence obtain the most skillful ensemble mean field. A part of our research goal is to develop such a field.

With this goal in mind, we will suggest in this paper a new technique for reducing the cost of dynamical downscaling of ensemble data. We used the Twentieth-Century Reanalysis dataset (Compo et al. 2011) as global ensemble atmospheric forcing data and the Scripps Institution of Oceanography (SIO)/Experimental Climate Prediction Center (ECPC) Global Spectral Model (GSM) with the spectral-nudging technique as a dynamical downscaling model. Global dynamical downscaling is essentially the same as regional downscaling, but uses a global model instead of a regional model and utilizes the spectral nudging to constrain the large-scale atmospheric fields. We tested the use of historical global ensemble data assimilation for global dynamical downscaling to evaluate the results over the whole globe and without region-specific biases.

In the next section, we will describe a new method called incremental correction of a single member (ICS) for dynamical downscaling. Then we will describe the data used, the model, and the experimental specifications in section 3. In section 4, the results with and without ICS will be shown by focusing mainly on surface variables. A discussion about the dynamical imbalance caused by ICS and the applications of the method will be given in section 5, and, finally, a summary and conclusions are presented as section 6.

2. Development of incremental correction of a single member by seasonal ensemble mean

Herein we present a new method called incremental correction of a single member (ICS) for dynamical downscaling. The procedure is somewhat similar to the work of Misra and Kanamitsu (2004), who corrected outer boundary forcing using a systematic error estimate, and that of Kawase et al. (2008), who applied the difference in the decadal average of current and future global change simulations to present-day global reanalysis data and then applied dynamical downscaling to obtain the regional-scale impact. The procedure proposed in this study is to correct a selected global member in such a way that the seasonal mean equals the ensemble mean. Dynamical downscaling is then applied using the corrected global data. The choice of the particular global member is a study in itself, and the sensitivity of the resulting simulation to the selection of the global member also requires investigation. In this study, arbitrary random choice is adopted, and different choices of a single member will be investigated.

As will be described later, this method modulates the low-frequency part of the global model circulation and leaves the high-frequency part as it is. The correction of global forcing fields is performed by following the equation
e1
where F is the full field of a physical variable (i.e., wind speed, temperature, humidity, and surface pressure), n is an ensemble member, angle brackets indicates the ensemble mean, and the overbar indicates the 1-month running mean. The downscaling is performed using as a lateral boundary forcing. A schematic representation is shown in Fig. 1. Note that in practice Eq. (1) is applied for all prognostic variables at all horizontal and vertical grids at once and no spatial filtering is used.
Fig. 1.
Fig. 1.

Schematic representation of the incremental correlation method for a single ensemble member toward the ensemble mean field. The horizontal and vertical axes indicate the time and the value of the atmospheric parameter (wind speed, temperature, etc.), respectively. The black and red thick lines represent the state before and after the incremental correction, respectively. The increment (gray-shaded area) was calculated by differencing the monthly running mean of the ensemble mean and a single member . The increment was then added to the single member.

Citation: Monthly Weather Review 141, 9; 10.1175/MWR-D-12-00271.1

The corrected fields have two important characteristics: 1) the low-frequency parts in the time dimension (specifically on monthly scales) of the prognostic fields are the same as those of the ensemble mean fields and 2) the high-frequency parts in the time dimension (specifically less than monthly scales) of the prognostic fields are the same as those of the single member. If the probabilistic distribution of all ensemble members for all the prognostic fields is regarded as being somewhat Gaussian, long-term averages of the correction would be close to zero. In other words, the dynamical imbalance caused by this correction in a snapshot will be canceled out as time proceeds. Furthermore, if the correction is small enough, the excited dynamical imbalance is also small anyway. In the discussion section below, the issue of dynamical imbalance will be investigated together with the degree of correction.

It should be noted that the procedures of ICS are purely preprocess handling, serving as a preparation step for the atmospheric model's time integration. Furthermore, the computational cost required by this method, including the overhead for data collection, is quite small compared with that of the model's time integration. What one has to do is collect ensemble mean data (atmospheric boundary conditions) and data for a specific single member for a target period. Because the method is a preprocess step that is independent of the model itself, it can be implemented with any other regional (or global) dynamical downscaling applications.

Altering the high-frequency disturbance to make the seasonal mean the same as the ensemble mean is an alternative to this method. This is not straightforward, but it may be possible by selecting other global ensemble members that have different high-frequency disturbance development patterns or by correcting the seasonal mean as the global model is integrated, which may act as a perturbation and trigger high-frequency transients, while keeping the seasonal mean of one member the same as that of the ensemble mean. These methods need to be tested and examined in future studies.

3. Data, model, and experiments

a. Twentieth-Century Reanalysis dataset

Version 2 of the Twentieth-Century Reanalysis (20CR) dataset consists of 6-hourly ensemble fields of 56 members with ensemble Kalman filter assimilation for the period 1871–2008 (updated until 2010 in 2012). The National Centers for Environmental Protection (NCEP) Global Forecast System (GFS) is used as the prediction model of 20CR and the resolution is T62 (about 180 km) and 28 sigma levels. For more detail about 20CR, refer to Compo et al. (2011). Every 6 h, we used raw 6-hourly snapshot files that contained spectral coefficients for zonal and meridional wind speed (U and V), temperature T, specific humidity q in all 28 sigma layers, and surface pressure Ps and topography. Thus, we did not lose any information associated with interpolation, either horizontally or vertically. The 20CR dataset usually provides only ensemble mean and spread fields for all prognostic and diagnostic variables, but we utilized the original variables from all 56 members. These data were downloaded from the National Energy Research Scientific Computing Center (NERSC) high-performance storage system (HPSS) archives.

b. Global Spectral Model and spectral nudging

In this study, we use the SIO ECPC GSM. The GSM was based on the medium-range forecast model used at NCEP for making operational analyses and predictions (Kanamitsu et al. 2002). The model incorporates state-of-the-art physics packages. Longwave and shortwave radiation (Chou and Suarez 1994), relaxed Arakawa–Schubert convective parameterization (Moorthi and Suarez 1992), nonlocal vertical diffusion (Hong and Pan 1996), mountain drag (Alpert et al. 1988), and shallow convection (Tiedtke 1983) are all included. The land scheme is the latest Noah land surface model scheme developed by NCEP and the National Center for Atmospheric Research (NCAR) (Ek et al. 2003). Because they have the same origin, GSM in this study and GFS used in 20CR are similar to each other particularly in their dynamical processes, but there are some differences in physical processes.

Note that actually we turn the stable water isotope physics on (namely IsoGSM; Yoshimura et al. 2008) when we run the GSM. The isotopic species are perfectly passive tracers, so the general circulation is not altered with or without the isotopes. We will eventually investigate the isotopic parameters in a subsequent paper.

To input the 20CR atmospheric fields as the constraint, we used the global spectral-nudging technique introduced by Yoshimura and Kanamitsu (2008). They showed that a type of spectral-nudging technique called the scale-selective boundary condition (SSBC; Kanamaru and Kanamitsu 2006) performs very well with a global model. They found that the nudging works particularly well when wind fields larger than 2000 km on the horizontal scale were nudged.

c. Specification of experimental settings

As we noted previously, we use the GSM with the global spectral-nudging technique. The critical nudging length is set at 2000 km, and the nudging strength α is set at a constant 0.9 for all 28 model layers. The nudged variables are the zonal and meridional wind and temperature. The target resolution is set at T62 (about 200 km). One may speculate that this resolution is not appropriate for the purpose of “downscaling” given that the 20CR's resolution is also T62. However, the nudging technique uses only scales larger than 2000 km, so the findings from our experiments are transferrable to globally or regionally higher resolutions of any dynamic downscaling application.

The target period of the experiments was set as 1871–2008, which is the coverage era of the 20CR dataset. The 20CR's ensemble spread continuously decreases with time, so we were able to examine cases with large and small ensemble spreads. For a representative period with a large ensemble spread, we used 1871–73. Similarly, the period of 1981–83 was used for a period with a small ensemble spread. The ensemble mean of major diagnostic fields (precipitation, 10-m wind, 2-m air temperature, and 500-hPa height) from 20CR were assumed as the truth.

We first executed a global dynamical downscaling run with atmospheric large-scale atmospheric forcings from the ensemble mean fields (EM run) for the whole 138 yr of study. Then, we conducted a similar run with the ICS method (ICS run), also for 138 yr. To examine the impact of the arbitrarily chosen ensemble member, we conducted a set of two 3-yr (1871–73 and 1981–83) simulations with another arbitrarily chosen different member (ICS2 run). To compare the experiments with the conventional brute-force experiments, six dynamical downscaling experiments with six different original single members were conducted for the same two periods. Statistics for each individual member were calculated, and the average is plotted in the following figures and labeled as S1. Two types of ensemble means were calculated by using three runs (S3) or all six runs (S6). Note that the difference between the three- and six-run choices was not significant to the conclusions.

4. Results

a. Dynamical downscaling with ensemble mean fields (EM run)

We first present the results of the EM run, in which ensemble mean fields were directly used as large-scale atmospheric forcings. Figure 2 shows the climatological seasonal precipitation for the early (1871–73) and the later (1981–83) periods and their differences. As would be expected, the results were obviously damaged. The biggest problem appeared in the precipitation over the northern part of the Pacific Ocean in December–February (DJF) of the early period (Fig. 2a), as seen by comparing with the original 20CR data (figure not shown), where a lack of precipitation exists over the northern Pacific Ocean. In contrast, no such damage is apparent in the later period of 1981–83 (Fig. 2b). Therefore, a spurious increasing trend was observed in this area (Fig. 2c).

Fig. 2.
Fig. 2.

Climatological seasonal mean precipitation from the EM run: (a)–(c) the results for the boreal winter (DJF) and (d)–(f) the same but for the boreal summer (JJA). Results for the (a),(d) early period (1871–73); (b),(e) recent period (1981–83); and (c),(f) differences between the recent and early periods. The global averaged value (glbave) is shown at the top of each panel.

Citation: Monthly Weather Review 141, 9; 10.1175/MWR-D-12-00271.1

We suspect that these flaws were actually due to the degree of the ensemble spread. Because the ensemble spread was larger in the earlier period, the synoptic-scale details in the ensemble mean fields were damped away. In reality, a large part of the winter precipitation over the northern Pacific is controlled by changes in synoptic circulation patterns (i.e., frequent temporal changes in the pressure and wind fields at a particular location), but these patterns were diluted in the EM run so that much less precipitation appeared. Figure 3 shows DJF averages of column moisture divergence for the EM run. The moisture flux can be decomposed into its mean and transient components by Reynolds averaging as
e2
where q is the specific humidity, u is the zonal wind speed, and the overbar and prime indicate the mean and the departure from the mean (the transient term), respectively, for a certain averaging period (i.e., monthly). The divergence can also be decomposed into mean and transient components and those components are shown in Fig. 3. The contribution from the transient term was not negligible in some specific areas in the later period, as shown in Fig. 3f. However, as shown in Fig. 3c, the contribution was almost zero over the entire globe in the earlier period. It is interesting to note, as shown in Fig. 3c, that there was a stronger signal from the transient contribution over the northwestern Atlantic. This indicates that the ensemble spread was not extremely large as a result of the existence of observations in this period for these regions (due to Europe–North America shipping connections). These figures clearly indicate a part of the reason why a dynamical downscaling simulation could suffer as a result of the ensemble mean boundary conditions.
Fig. 3.
Fig. 3.

Seasonal (DJF) mean of moisture divergence in the EM run: (a),(d) the total divergence, (b),(e) the part derived from long-term averages, and (c),(f) the part derived from the transient terms; (a)–(c) shows the earlier period (1871–73) and (d)–(f) the recent period (1981–83).

Citation: Monthly Weather Review 141, 9; 10.1175/MWR-D-12-00271.1

b. Dynamical downscaling with incremental correction of a single member (ICS run)

Similar to Fig. 2, Fig. 4 shows the seasonal climatological precipitation from the ICS run, which is a global model integration toward a single ensemble member that was modified to have the identical monthly circulation fields as the ensemble mean. Figure 4a clearly shows improvement compared with Fig. 2a over the northern Pacific Ocean, indicating that the transient components of moisture flux (more specifically, wind) were much better forced.

Fig. 4.
Fig. 4.

As in Fig. 2, but for the ICS run.

Citation: Monthly Weather Review 141, 9; 10.1175/MWR-D-12-00271.1

Figure 5 shows the column moisture divergence. As shown in Fig. 5c, there are obvious improvements in the transient contribution to the total divergence in the earlier period, particularly over the northern Pacific. Though the transient contribution of moisture divergence (Fig. 5c) is smaller than the mean contribution (Fig. 5b), the total precipitation over midlatitudes, particularly the northern Pacific, is large. On the other hand, for the later period, the transient contribution (Fig. 5f) is already similar to that of the EM run (Fig. 3f); therefore, the precipitation was better simulated. That is, because in the EM run the ensemble spread is smaller during the later period (due to bigger constraints from the observation data), the high-frequency variability of the atmospheric fields is kept in the ensemble mean fields.

Fig. 5.
Fig. 5.

As in Fig. 3, but for the ICS run.

Citation: Monthly Weather Review 141, 9; 10.1175/MWR-D-12-00271.1

c. Comparisons with the conventional brute-force method

Our new method, dynamical downscaling with ICS, has the intended purpose of reducing the cost of the dynamical downscaling of the ensemble mean fields. Thus, we evaluated the method against the conventional brute-force method, that is, multiple runs of dynamical downscaling with the direct use of a single ensemble member. As described in the previous section, we randomly picked 6 of the 56 members and used these atmospheric fields as the large-scale atmospheric forcings. The diagnostic variables of the downscaled fields were then averaged and compared with the “truth” (i.e., the original 20CR ensemble mean fields). Run S6 includes the ensemble mean fields of all six downscaled ensembles. S3 is the average of only three members and S1 has no ensemble averaging.

Figure 6 shows the area-weighted spatially averaged root-mean-square deviation (RMSD) for the seasonal [DJF, March–May (MAM), June–August (JJA), and September–November (SON)] mean 500-hPa height between the various experiments and the truth (20CR ensemble mean fields). Global (top row), Northern Hemispheric (middle row), and Southern Hemispheric (bottom row) averages for the earlier period 1871–73 (left column) and the more recent period 1981–83 (right column) are illustrated in Fig. 6. Note that the vertical ranges for the left and right columns are different to make the differences clearer. During the earlier period, which had a large ensemble spread, the RMSD of any S1 run was largest. This fact indicates that a dynamical downscaling run with a single member has lower reliability compared with the ensemble mean. The average departures were about 20–24 m. These departures could be decreased by averaging the multiple dynamical downscaling runs; the departures were nearly halved in S3 (11–15 m) and were only about one-third as large in S6 (8–10 m).

Fig. 6.
Fig. 6.

Spatially averaged RMSD in 500Z against the original 20CR ensemble mean. The EM, ICS, S1, S3, S6, and ICS2 runs are shown as black open circles, green closed circles, blue open squares with error bars, red closed squares, pink crosses, and violet open circles, respectively. S1 has the error bars because there were six patterns in the S1 experiment. Results are shown for (a)–(c) the early period (1871–73) and (d)–(f) the recent period (1981–83). (a),(d) The global-averaged RMSDs, and the (b),(e) Northern Hemisphere and (c),(f) Southern Hemisphere averages. The temporal mean values of each run are shown in parentheses in the legend of symbols.

Citation: Monthly Weather Review 141, 9; 10.1175/MWR-D-12-00271.1

The EM run showed the least departure (2–3 m) because the ensemble mean circulation fields (U, V, and T) were directly forced onto the model as boundary conditions. However, this does not necessarily indicate that the EM run would also perform best for the other diagnostic variables. In particular, the EM run has a large weakness in precipitation (as shown before). In the ICS run, the departure was decreased to 8–10 m, which is comparable to the S6 result. This clearly indicates that the ICS method was a success. It reduced the computational cost of dynamical downscaling of the ensemble mean field by ⅙ because an ICS run requires only a single run compared with six runs to achieve S6.

The ICS2 run, which was the same as the ICS run except for using a different single ensemble member as the perturbation part, showed almost the same RMSD (8–10 m). This means that the choice of the single member did not have a big influence on the seasonal mean 500-hPa geopotential height. It also demonstrates the robustness of the ICS method.

For the recent period (1981–83), all of the experiments had much lower RMSDs. However, even though the ensemble spread of 20CR in this period is much smaller, the S1 runs showed the largest departure from the EM run (Figs. 6d–f). This is also the reason that S3 and S6 came quite close to the truth, as did the ICS run.

Figure 7 shows similar metrics to those in Fig. 6, but for precipitation. As already discussed in the previous sections, the EM run deteriorates with respect to the hydrological cycle. It is obvious that the RMSDs of the EM run were the largest over the globe and for the Northern and Southern Hemispheres, mainly due to the lack of high-frequency variability in the wind speed. The spatially averaged RMSD was about 0.006 mm day−1. In the ICS run, the RMSD was much smaller at about 0.004 mm day−1, which is comparable to that of the S3 run and definitely better than any of the S1 runs (about 0.005 mm day−1). However, unlike the 500-hPa height results, the RMSD of ICS is slightly higher than the S3 and S6 results (about 0.0035 mm day−1). This implies that the ICS method reduced the computational cost of dynamical downscaling of the ensemble mean field by around from ½ to ⅓.

Fig. 7.
Fig. 7.

As in Fig. 6, but for precipitation.

Citation: Monthly Weather Review 141, 9; 10.1175/MWR-D-12-00271.1

The ICS2 run showed almost the same RMSD as did the ICS run, so the seasonal precipitation amount was not influenced very much by differences in high-frequency variability. The S6 run showed slightly better performance than did ICS/ICS2. Similar to the RMSD for 500-hPa height, the RMSDs in the recent period (Figs. 7d–f) were smaller for all runs, and the implications from the results were very similar to those from the earlier period.

The annual averaged precipitation for all of the experiments and for the 20CR ensemble mean from 1871–2008 is shown in Fig. 8. This figure clearly illustrates the significant artifact of the EM run, a continuously increasing precipitation trend. This is due to the fact that the ensemble spread decreased through time as the observation network improved. As the ensemble spread becomes smaller, the ensemble mean wind fields retain the transient components better; therefore, the moisture divergence/convergence that occurs at middle latitudes is represented more appropriately. Compared with the EM run, the ICS run showed time series much closer to the original 20CR. All six of the S1 runs with direct use of six different single members are also plotted in Fig. 8 by gray lines and they do not show any notable malfunction for the annual global averaged precipitation.

Fig. 8.
Fig. 8.

Global mean precipitation by each experiment from 1871 to 2008. The 20CR simulation (green), the EM run (black), and the ICS run (blue) are shown for the entire period. Those runs with the direct use of single members (six S1s) are shown only for 1871–73 and 1981–83 with gray lines.

Citation: Monthly Weather Review 141, 9; 10.1175/MWR-D-12-00271.1

The global RMSD of the seasonal mean surface wind (U10m) look like those in Fig. 6 (figure omitted). The S1 runs had the largest RMSD, and the EM run performed the best. The ICS run had a spatial average RMSD of 0.6–0.7 m s−1, and the other runs also showed results similar to those in Fig. 6. The performance of the ICS run (and the ICS2 run) was similar to that for the S6 result. The 2-m air temperature RMSDs are, unlike the case for surface wind, similar to those of precipitation (figure omitted); that is, the EM run becomes the worst-performing dynamical downscaling. As for the case of precipitation, this is due mainly to a malfunction in the moisture circulation in the EM run. Because moisture was not properly conveyed, causing less precipitation in the EM run, the departure of the surface-air temperature from the truth became larger. Another interesting feature is the high contrast between the Northern Hemisphere and Southern Hemisphere. The majority of the surface in the Southern Hemisphere is ocean, and in our experiments, sea surface temperatures were input from 20CR. Therefore, there is almost no departure in the 2-m temperature between all the experiments and the 20CR ensemble mean. The performance of the ICS and ICS2 runs was similar to that of S6.

5. Discussion

a. Conservation of dynamical balance by ICS

In this section, we evaluate how much ICS modifies the atmospheric fields and whether ICS violates the conservation of dynamical balance in the atmosphere or not. The global averages of the absolute increment of zonal wind speed, temperature, and specific humidity for Januaries in 1871 and 1981 are shown in Fig. 9. The figure for meridional wind speed is similar to that of zonal wind (Fig. 9a), so it is omitted. As expected, the degree of correction is larger in the earlier period, since the discrepancy between the single member and the ensemble mean was larger. The latitude-weighted global-averaged absolute increment is about 1 m s−1 for zonal wind at 1000 hPa in January 1871, but gradually increased up to more than 3.5 m s−1 at the 200-hPa level, and decreased again for higher levels (Fig. 9a). In January 1981, the correction is less than 0.3 m s−1 at 1000 hPa, and it hits its maximum of 2.0 m s−1 at the 150-hPa level. For temperature (Fig. 9b), the averaged absolute correction is about 0.8 K (0.3 K) in the troposphere in 1871 (1981). For specific humidity (Fig. 9c), since the amount of moisture available at lower levels is much greater, the absolute increment is gradually decreased at higher levels. The degree of the averaged absolute increment is 0.4 g kg−1 (0.2 g kg−1) at most in 1871 (1981).

Fig. 9.
Fig. 9.

Vertical profiles of the global averaged absolute increment by ICS during Januaries of 1871 (black lines) and 1981 (green lines) for (a) zonal wind speed, (b) air temperature, and (c) specific humidity.

Citation: Monthly Weather Review 141, 9; 10.1175/MWR-D-12-00271.1

Because ICS forces such a large degree of modification for wind, temperature, and humidity, we have to check whether the atmospheric dynamical balance is conserved in good shape. We use the following nonlinear balance equation (NLBE; Charney 1955), and the residual term R indicates the atmospheric imbalance at each grid point and level:
e3
where f is the Coriolis parameter, is the Laplacian operator, Ψ is streamfunction, and Φ is geopotential. A larger R term indicates larger artificial dynamic forcing in the atmosphere. Figure 10 shows the global averages of the absolute R term at different levels. Interestingly, the dynamical balance was best conserved in the ensemble mean fields in both 1871 and 1981. By comparing the ensemble mean fields between 1871 and 1981, the dynamical conservation is more satisfied in 1871. This fact indicates that by averaging ensemble members, the dynamical imbalance that existed in each single member was canceled out. This is essentially similar to the fact that the ensemble mean fields have the best skill in midterm forecasts due to the noise in each single member being canceled out and only signals being retained. The more important point is that the degrees of dynamical imbalances are almost identical with the original (uncorrected) single member and the ICS member [in 1871, slightly larger imbalance is observed in the upper troposphere (200–300 hPa) in ICS, as shown in Fig. 10a]. This clearly confirms that the dynamical balance is well conserved after the ICS treatment.
Fig. 10.
Fig. 10.

Global-averaged absolute R term in NLBE in the original single member (Org), the modified single member by ICS (ICS), and the ensemble mean (EM) for January (a) 1871 and (b) 1981.

Citation: Monthly Weather Review 141, 9; 10.1175/MWR-D-12-00271.1

Atmospheric dynamic balance can be evaluated with the temporal tendency of the surface pressure with short-term atmospheric prediction (Lynch and Huang 1992). We have executed a set of many (starting from various timings) short-term GSM forecast runs with three types of global data (i.e., ensemble mean, original single member, and ICS member) as the initial conditions. The global-averaged absolute tendency of surface pressure is sufficiently low [around 1.0 hPa (3 h)−1] and stable throughout 240 forecast hours in all runs (figure omitted), indicating that the dynamical balances in these three data are sufficiently conserved. These results are consistent with the NLBE results above.

b. Future directions

The methodology proposed in this study has direct practical implications for the dynamical downscaling of operational ensemble seasonal forecasts and/or ensemble data assimilation because it produces physically and dynamically consistent small-scale features corresponding to the most likely future state obtained by ensemble averaging. Additionally, several fundamental scientific questions are associated with the methodology proposed here. First, there is the question of ensemble averaging. Assuming that the ensemble seasonal mean is the single best possible forecast/analysis, do many members lead to the given seasonal mean? If many do, which member is most likely? How can this “most likely” member seasonal mean be associated with a probabilistic distribution of precipitation and near-surface temperature? How does this probability of the diagnostic fields relate to the probability of the prognostic fields with regard to the nonlinear relationship between them? Are the two probability distributions different? If so, what is the mechanism that modifies them?

Another basic and related issue is the makeup of the seasonal mean. Is it made up of a few strong transient disturbances, or is it made up of very slowly changing low-frequency disturbances? The answer is probably case dependent, but this question is strongly related to the success of the proposed method, and it may also be strongly related to predictability on a seasonal time scale. This question can be answered by analyzing the frequency spectrum of disturbances during the model-integration period. Low-frequency disturbances may dominate during warm seasons, whereas high-frequency disturbances may dominate during cold seasons. The dominating frequency may also vary significantly with the tropical SST anomaly. Thus, our new method of incremental correction of a single ensemble member (ICS) is closely connected with this problem. We leave these issues for future study.

Furthermore, this method has the potential to be used for multimodel ensemble projections of the future climate. However, it poses at least the following difficulties. 1) Although the multimodel ensemble seems to be the most skillful in seasonal forecasting (e.g., Matsueda and Tanaka 2008), it has not been proven yet that the multimodel ensemble of climate projections offers the best estimate of the future climate. The reliability of the climate models is not uniformly distributed (e.g., Min et al. 2007); therefore, it may not be best to use the ensemble mean fields to downscale dynamically. 2) Given that each model has different bias characteristics, the choice of the single member for high-frequency perturbation may be more sensitive to the results than our test cases in this study using single-model ensemble members. Although these issues appear to be critical, it is worthwhile investigating the feasibility of the method for multimodel climate projections in the future because of the very large advantage in computational efficiency.

6. Summary and conclusions

In this paper, we described a new economical method for dynamically downscaling the ensemble mean field, which is regarded as the most skillful data for ensemble seasonal forecasts or ensemble data assimilation. The conventional brute-force approach, which has frequently been used to date, simply applies dynamical downscaling to some or all of the ensemble members and obtains the ensemble mean of the downscaled fields, but this approach is expensive.

Our new method is called incremental correction of a single ensemble member (ICS). In this method, increments between monthly running values of the ensemble mean and a single member are added to the single member field. The corrected fields have the following characteristics: 1) the low-frequency parts (monthly scales) of the prognostic fields are the same as those of the ensemble mean fields and 2) the high-frequency parts (less than monthly scales) of the prognostic fields are the same as those of the single member.

We applied the ICS method to the dynamical downscaling of Twentieth-Century Reanalysis (20CR) data for 1871–2008. The Global Spectral Model (GSM) in T62L28 with a global spectral-nudging technique was used. For comparisons, dynamical downscaling runs were done by direct use of the ensemble mean fields and by direct use of six different ensemble members in the conventional brute-force way (S6 run).

Direct use of the ensemble mean fields as the atmospheric lateral boundary forcing apparently failed to simulate the hydrological cycle correctly. Specifically, there was too little high-frequency variability at the northern part of the North Pacific, so the precipitation there was too low. We believe this problem was caused by too little influence of the transient components in moisture divergences due to a larger ensemble spread and damped high-frequency fluctuations in the wind fields.

The ICS method dramatically improved the hydrologic cycle results. For the 500-hPa geopotential, precipitation, surface wind speed, and surface air temperature fields, the departure of the ICS run from the original 20CR ensemble mean fields became quite similar to the S6 results. Therefore, it is reasonable to state that the computational requirement of our new incremental correction method could be as low as from ⅙ to ½ that of the brute-force method.

This method has direct practical implications for the dynamical downscaling of not only operational ensemble seasonal forecasts and ensemble data assimilation but also multimodel ensemble climate projections. To do so, we have to conduct further investigations into the characteristics of the distributions of ensemble members in each case. Such investigations would be worthwhile in terms of cost–benefit outcomes in the future.

Acknowledgments

This study was conducted under the SOUSEI program of Ministry of Education, Culture, Sports, Science and Technology in Japan. A part of this research was also funded by the Japan Society for the Promotion of Science (JSPS) Grant 23686071. The numerical simulations were partly performed with computing resources at the Center for Observations and Prediction at Scripps (COMPAS) and at TeraGrid. The authors thank Dr. Gil Compo for his comments and support from the initial stage of this study.

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