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Keywords:

  • Tropical Cyclone Statistics Retrieval;
  • Climate Estimation;
  • Climate Prediction

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methodology
  5. Results
  6. Summary and Discussions
  7. Acknowledgments
  8. References

When observations are assimilated into a high-resolution coupled model, a traditional scheme that preferably projects observations to correct large-scale background tends to filter out small-scale cyclones. Here we separately process the large-scale background and the small-scale perturbations with low-resolution observations for reconstructing historical cyclone statistics in a cyclone-permitting model. We show that by maintaining the interactions between small-scale perturbations and successively corrected large-scale background, a model can successfully retrieve the observed cyclone statistics that in return improve estimated ocean states. The improved ocean initial conditions together with the continuous interactions of cyclones and background flows are expected to reduce model forecast errors. Combined with convection-permitting cyclone initialization, the new high-resolution model initialization along with the progressively advanced coupled models should contribute significantly to the ongoing research on seamless weather-climate predictions.

Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methodology
  5. Results
  6. Summary and Discussions
  7. Acknowledgments
  8. References

Incomplete understanding on physical processes and imperfect numerical implementation make high-resolution climate models biased [Delworth et al., 2012], and modeled tropical cyclone (TC) climatology and variability turn out to be significantly different from the real world [Gualdi et al., 2008; Zhao et al., 2009; H.-S. Kim et al., Tropical cyclone simulation and response to CO2 doubling in the GFDL CM2.5 high-resolution coupled climate model, submitted to Journal of Climate, 2013]. In the weather-climate community, scientists attempt to estimate the historical climatological features and variability by assimilating observations such as atmospheric temperature and winds as well as oceanic temperature and salinity into a coupled model [e.g., Zhang et al., 2007; Sugiura et al., 2008], including the study on simulated TC climatology [Mori et al., 2013]. When conventional measurements of atmospheric states which do not resolve TCs are assimilated into a high-resolution model, the data projection relying on a covariance assumption tends to filter out small-scale information in the model. For weather forecast purpose, it is a common practice for one to impose a vortex in the observation-corrected background fields (i.e., “bogus” storms) for TC initialization [e.g., Kurihara et al., 1993, 1995]. When a high-resolution coupled climate model is able to generate its own TCs, the interactions between TCs and background climate signals may play an important role for accurate climate estimation and prediction initialization. Traditional “bogus” techniques for short-term weather predictions do not meet the demand of climate studies owing to this inconsistency. Here we explore two key questions one needs to address when observed data are used in conjunction with a high-resolution coupled model: (1) What method can one use to correct model fields without causing a significant dissipation to model self-generated TCs so that the observation-corrected model can produce realistic TC statistics? and (2) What is the impact of the corrected TC statistics on climate state estimation and the implications to climate prediction?

Methodology

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methodology
  5. Results
  6. Summary and Discussions
  7. Acknowledgments
  8. References

This study uses a newly developed global high-resolution coupled model, called CM2.5, at Geophysical Fluid Dynamics Laboratory [Delworth et al., 2012]. The atmospheric component has an approximately 50 km horizontal resolution and 32 vertical levels, formulated on a “cubed-sphere” grid described on six sides of a cube projected on the sphere [Putman and Lin, 2007]. The oceanic component has a horizontal resolution ranging from 28 km at the equator to 8–11 km at high latitudes to enhance the representation of processes such as high-latitude deep water formation, with 50 vertical levels, allowing an explicit simulation of some mesoscale eddies in the ocean, particularly at lower latitudes. The simulated climate in CM2.5 showed significant improvement over the tropics compared to the previous coarse-resolution CM2.1, including a reduction of biases in the seasonal variation of the Intertropical Convergence Zone and an improved simulation of some aspects of the El Niño–Southern Oscillation and its teleconnections, as well as a relatively realistic regional rainfall over the Amazon, Sahel, and Indian monsoon regions and climate over the tropical North Atlantic [Delworth et al., 2012; Doi et al., 2012].

This study employs a simple nudging method to incorporate gridded atmospheric data and sea surface temperature (SST) data into the CM2.5 model. The SSTs are the product of satellite measurements using the infrared channels of AVHRR (advanced very high resolution radiometer) maintained by NCDC (National Climate Data Center), and the atmospheric winds and temperatures are the reanalysis product of NCEP/NCAR (National Centers for Environmental Prediction/National Center of Atmospheric Research) [Kalnay et al., 1996]. The atmosphere nudging scheme has been described in Gall et al. [2011], only nudging the principal dynamical fields such as winds and temperature as well as surface pressure, with a nudging e-folding time scale of 6 h. The SST nudging is performed in the tropical ocean (40°S–40°N), with the nudging e-folding time scale of 3 days. To maintain the ocean stratification at high latitudes, no SST nudging beyond 60°S(N), and the nudging coefficient is ramped to zero from 40°S(N) to 60°S(N).

The coupled model state at 00 UTC of 1 January 1999 was produced by a historical simulation using all forcings starting from 1861, which is initialized from the control simulation described by Delworth et al. [2012]. We start the assimilation experiments from 1 January 1999 and end up at 1 January 2012. The NCEP reanalysis data with the T62L28 model (62 horizontal triangle truncation and 28 vertical levels) are used for the assimilation period. Inspired from the “spectral nudging” idea [Waldron et al., 1996; von Storch et al., 2000] which has been successfully applied to dynamical downscaling with regional models [von Storch et al., 2000; Knutson et al., 2008; Peng et al., 2010], we design a simple but easily implementable Gaussian smoother to separate the “large-scale” background and the “small-scale” perturbations in the atmosphere for global climate assimilation studies. The Gaussian smoother is applied to the model fields before they are adjusted by the observations at each analysis step as

  • display math(1)

where i, j represent the current model grid and a hat represents the weighted average result using K neighboring points including (i,j) itself (indexed by k). The normalized weighting coefficient wk is defined as

  • display math(2)

where dk is the distance between the locations of points k and point (i, j) and d0 is the e-folding distance that controls the strength of the smoother. Given the relatively even grid box area of the cubed-sphere mesh system [Putman and Lin, 2007], dk and d0 can be calculated based on grid indices. For the purpose of tropical cyclone (TC) studies with this TC-permitting model, here we use the typical tropical cyclone radius (500 km) as the scale to define d0 so that the model is allowed to create its own TCs based on observation-corrected large-scale flows. In the future, when the representation of observations is enhanced, the value of d0 can be refined to reflect the representation of observations and the scale of activities of interests for which the model can resolve. Once d0 is defined, the smoother is carried out in a square grid array that is centered at (i,j). In this study, the smoothed results inline image (the flows whose spatial scales are greater than 1000 km) represent the large-scale background and the residual between the full values x and inline image represents the small-scale perturbations. The background adjustment scheme only applies low-resolution observations to inline image. When all inline image fields are adjusted by the observations at each analysis step, the small-scale perturbations are added back to form the full values of the observation-updated fields. Without demanding the transformation between spectral and grid spaces, this simple Gaussian smoother and associated background adjustment scheme only has a minimal computational resource requirement and thus is particularly suitable for global climate data assimilation studies with the irregularly spaced climate observing system, especially when the coupled model resolution becomes higher and higher.

We evaluate the capability of a data assimilation scheme through comparing the produced TC statistics with “observations.” The observations are based on the International Best Track Archive for Climate Stewardship (IBTrACS) [Kruk et al., 2010]. The IBTrACS data set is the results of postseason reanalysis of a storm's position and intensity from all available data sources including ship, surface, and satellite observations. It provides the best observational data set for global TCs [Knapp et al., 2010]. The TC detection and tracking algorithm used in this model follows the work of Zhao et al. [2009], Knutson et al. [2007], and Vitart et al. [1997] which employs 6-hourly sea level pressure, surface winds, 850 hPa vorticity, and 300–500 hPa mean temperature. Consistent with previous studies [Knutson et al., 2007; Zhao et al., 2009], we use 17 m/s and 3.5E-5 as the maximum surface wind speed and vorticity threshold for TC detection. The tracking and detection algorithm is consistent with those methods used for determining the observed TCs in IBTrACS [Kruk et al., 2010; Knapp et al., 2010].

Results

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methodology
  5. Results
  6. Summary and Discussions
  7. Acknowledgments
  8. References

We first analyze the performance of the coupled model on TC simulation. The model simulation uses historical greenhouse gas and natural aerosol (GHGNA) radiative forcings, and therefore, the model calendar refers to the GHGNA records. Figures 1a and 1b present the observed and model simulated spatial distributions of TC genesis locations. Generally consistent with other studies on the TC analysis of the CM2.5 model (e.g., H.-S. Kim et al., submitted manuscript, 2013), the model overproduces the total number of TCs globally. In particular, it produces too many TCs in the central Pacific where the observations exhibit a gap between the West and the East Pacific. In the northwest Pacific, the modeled TCs tend to concentrate to the south of 25°N, while the observations show more cyclones developed to the north of 25°N. While the model significantly overestimates the TC frequency in the South Indian Ocean, it underproduces the Southwest Pacific TCs with genesis locations confined to the west of the dateline. In contrast to the excessive number of Pacific TCs, the model substantially underestimates the Atlantic TCs, especially in the main development region (10°–25°N and 80°–20°W), the Gulf of Mexico, and the Caribbean Sea. These basin-wide TC biases can also been seen in the time series of yearly TC count shown in Figure 2. There is no significant correlation between the simulated and the observed annual TC count in the West Pacific, the North Atlantic, and the entire global ocean.

image

Figure 1. Tropical cyclone (TC) genesis locations in the observations, model, and three assimilation analyses. The spatial distribution of TCs in (a) observations (OBS), (b) model simulation (MDL), (c) sea surface temperature constraint (SSTC), (d) SSTC plus traditional atmospheric data assimilation (SSTC + TDA), and (e) SSTC plus background atmospheric adjustment scheme (SSTC + BGA). The global TC records are taken from the IBTrACS (International Best Track Archive for Climate Stewardship) [Knapp et al., 2010; Kruk et al., 2010]. The algorithm of detecting and tracking model storms follows the earlier work of Vitart et al. [1997] and Zhao et al. [2009].

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image

Figure 2. The variations of tropical cyclone (TC) annual counts in two basins and global tropics. The time series of TC annual counts in the (a) tropical northwest Pacific (0–40°N, 120–180°E), (b) tropical North Atlantic, and (c) global tropics for OBS (black), MDL (dashed green), SSTCs (green), SSTC + TDA (blue), and SSTC + BGA (red). The three numbers by order in the parentheses of Figures 2a and 2b are the correlation coefficient between the modeled annual TC counts and the observations in experiments SSTC, SSTC + TDA, and SSTC + BGA. A star indicates the correlation value with the significance above 95% confidence level. A dash sign indicates no significant correlation existing.

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With the assimilation system described before, we first conduct a coupled data assimilation experiment in which only the model SSTs are constrained by the observations but the atmosphere remains free (denoted as SSTC). We now examine the impact of the observation-constrained SSTs on TC statistics. We conduct empirical orthogonal function (EOF) analysis to the SST anomalies over the tropical Pacific domain (120°E–80°W, 40°S–40°N) to understand the impact of the SST constraint on TC statistics in this model. The time series of some principle components (PCs) as examples are shown in Figures 3a and 3b (to facilitate the comparison between the traditional full value assimilation and the new background adjustment scheme, here we show PC1 and PC6 which will be discussed more later). As expected, while the model SSTs are constrained toward the observations in leading-order signals (compare the green line to the black line in Figure 3a), the distribution of simulated TC genesis frequency is improved dramatically (Figure 1c). Despite the overall improvement in spatial distribution of TCs, the temporal variation of annual TC count in the SST constraint case has insignificant correlation with the observations (compare the green line with the black line in Figure 2). This can be attributed to the large-scale atmospheric circulation biases generated by the model even with the constrained SSTs (although it is difficult to rule out the effect of internal noise with this single realization). Under the circumstance, the free atmosphere remains independent from the historical information (see the green lines in Figures 3e and 3f). Due to the feedback of the unconstrained atmosphere, the high-order SST signals are not well correlated with the observed signals (compare the green line to the black line in Figure 3b).

image

Figure 3. Principle component (PC) signals of anomalies of the sea surface temperature (SSTA), ocean mixing layer depth (MLDA), upper ocean (200 m) heat content (HC200) (1999–2011), and atmosphere wind shear (January 2003 to December 2003) in the observations, model, and three assimilation analyses. The time series of normalized (a and e) PC1 and (b, c, d, and f) PC6 indices of monthly SST anomalies in Figures 3a and 3b, monthly anomalies of ocean mixing layer depth in Figure 3c, upper ocean heat content Figure 3d, and 6-hourly wind shear [(u250–u850)2 + (v250–v850)2]1/2 anomalies in Figures 3e and 3f in the tropical Pacific domain (120°E–80°W, 20°S–20°N) in the assimilation experiments of SSTC (green), SSTC + TDA (blue), and SSTC + BGA (red). In Figures 3a–3f, the corresponding observational (AVHRR SST and NCEP/NCAR reanalysis wind shear) indices are plotted by black lines. For visualization, all ocean (atmosphere) indices are performed a 12 month (10 day) running smooth. The EOF1 and EOF6 explain about 53% and 2% for the variance of SSTA, 11.7% and 3.1% for MLDA, 32.3% and 2.1% for HC200, and 10.5% and 3.5% for wind shear anomalies.

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In addition to the SST constraint, we conducted traditional atmospheric data assimilation (TDA) to constrain the atmospheric state to observations (nudging the NCEP/NCAR reanalysis in this case) (denoted as SSTC + TDA). We find that while the traditional atmospheric data assimilation can constrain the model atmosphere to the reanalysis with a very high accuracy (compare blue lines to black lines in Figures 3e and 3f), most of the TCs in the model disappear (see Figure 1d), resulting very few TCs in annual count for all basins (blue lines in Figure 2). To understand why the traditional atmospheric data assimilation filters out the model TCs, we analyze the change of the values of the model state variable at the observational adjustment step. We use Figure 4a to illustrate schematically how a covariance model (color shaded) projects an observational increment at the observational location (denoted by a black asterisk) to the neighboring model grid points and demonstrate the covariance model in assimilation synthesizes the properties of observations and the numerical model. In Figure 4a, the model variable x distributed on the model space (denoted by red dots) is supposed to be adjusted by the observed value y by the anisotropic covariance (assuming larger around the top left point than around the bottom left point, for instance), while the shaded colors from green, grey to light-green schematically represent the decrease of covariance values. Theoretically, if both observations and the model contain TC information, an optimized assimilation scheme (efforts including covariance localization [e.g., Gaspari and Cohn, 1999; Houtekamer and Mitchell, 1998; Hamill et al., 2001; Anderson, 2012]) is able to produce consistent TC statistics and individual TC structures with observations. However, due to the current limitation on computational resources and climate data assimilation advances with coupled generation circulation models, the first step of global climate data assimilation studies is to reconstruct the historical TC statistics using conventional (coarse-resolution) observations. Figure 4b presents the change of the meridional component of wind at 10°N after an assimilation step in TDA (blue) based on the model first guess (green) due to restoring to the observation (black). It shows that restoring model values to the low-resolution observations makes small-scale perturbations dissipated and hence wipes out modeled TCs. Next, we describe an example how to optimally combine coarse observations with model dynamics for reconstructing TC statistics by separately processing the large-scale background fields and small-scale perturbations.

image

Figure 4. The filtering of small perturbations in traditional data assimilation (TDA) and the maintenance of small perturbations in background adjustment scheme (BGA). (a) The schematic of covariance (color shaded) projecting an observational increment (computed from the observed value y and the model background) at the observational location (denoted by a black asterisk) onto the model variable x distributed on the model space (denoted by red dots). The shaded colors from green, grey to light-green schematically represent the decrease of covariance values. (b) Zonal variations of v velocities at the bottom model level along with 10°N longitudes before (green) and after the first step of traditional data assimilation (TDA, blue) and background adjustment (red) analysis. The observations (the NCEP/NCAR reanalysis, denoted as OBS) are plotted by a black curve in Figure 4b.

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To maintain the modeled TCs, we employ the Gaussian smoother and implement the background adjustment assimilation scheme described in section 2 for the atmosphere. We denote this experiment as SSTC + BGA. We compare the leading-order signals in TDA and BGA in Figure 3. Generally, when the PC order is lower (PC1 and PC2, for instance), the difference of BGA and TDA is smaller, while the BGA-TDA difference becomes larger when the PC order is higher (representing more high-frequency signals). To facilitate the comparison between BGA and TDA for relatively significant signals, we show PC1 and PC6 in Figure 3. It is evident that the BGA assimilation approach reproduces the high accuracy of atmospheric state variable analysis (see the red and black curves of Figures 3e and 3f) while maintaining the small-scale perturbations in the model fields (compare the red curve to the blue curve in Figure 4b). The distribution of TC genesis frequency in the 13 year assimilation period is presented in Figure 1e, and the temporal evolution of annual TC count in the West Pacific, the North Atlantic, and the entire global tropical ocean is plotted in red curves in Figure 2. Compared to the SSTC case (Figure 1c), the SSTC + BGA better reproduces the spatial distribution of the TC genesis frequency (compare Figures 1e and 1a). In particular, the spatial patterns of TC genesis frequency in both the Pacific and Atlantic are improved significantly. Furthermore, after the spin-up, the model reproduces well the interannual variability of TCs in annual count in the West Pacific and North Atlantic basins as well as the global ocean (compare the red curve to the black curve in Figure 2). The correlation coefficients between modeled and observed TC frequency in both the West Pacific and North Atlantic increase from roughly 0.4 in the SSTC case to 0.8 (see the numbers in parentheses of Figures 2a and 2b). Associated with the response of subsurface heat content and feedback to TC activities, the SSTC + BGA spin-up time scale is 2–3 years (this will be discussed further when we analyze the subsurface ocean responses later). We notice that due to the spin-up effect, in 2001, except for the tropical North Atlantic, the SSTC + BGA-produced TC numbers in the other two examined basins are not better than the SSTC produced. We also notice that both SSTC and SSTC + BGA cases produce fewer TCs in the East Pacific than the observations, which may be associated with model defects. Compared to the SSTC case and observations, the SSTC + BGA case reduces the TC number in the area of the east of Indonesian, increases the TC number over the South Pacific and higher-latitude area of the South Atlantic. This is a result of assimilating the reanalysis data into the model. Further research work is required to identify the cause for the error between the BGA scheme and the defect of reanalysis data. For example, compared to the storms generated in other basins, the size of East Pacific TCs is significantly smaller [Chavas and Emanuel, 2010], and therefore, they may not be well resolved at this model's resolution. The e-folding distance in the Gaussian filter may be needed to be adjusted to better simulate TCs in this region. In addition, it is worth mentioning that beside the number and distribution, the statistics of TCs' intensity (i.e., wind speed and sea level pressure) are also important to represent the effects of TC activities in climate signal developing and maintaining. Such analyses will be conducted when the studied scheme is applied to the next generation coupled model that successfully resolves the interior structure of individual TCs.

The improvement of TC distribution and variability in SSTC + BGA suggests the importance of the observational constraint of atmospheric states for reconstructing the TC statistics by combining data with a high-resolution coupled model. Our results show that incorporating the NCEP/NCAR reanalysis data into a coupled model can greatly improve the SST signals. This suggests that a consistent coupled data assimilation scheme can better extract the climate signals (although the NCEP/NCAR reanalysis has its own model error as well as analysis error, and the analysis data are not exactly consistent with the observed SSTs).

Another interesting point is that while the SSTC + BGA produces nearly identical PC1 signals (explains about 53% of the variance) of SST anomalies with the SSTC + TDA, its PC6 (explains about 2% of the variance) is closer to the observation by 15% (measured by the reduced root-mean-square error from 12.5 to 10.7). Given the nearly identical atmospheric signals between the SSTC + BGA and SSTC + TDA (overlapped blue and red curves in Figures 3e and 3f), this improvement is most likely due to the TC feedback to SSTs in SSTC + BGA. Indeed, the signals in PC6 of the mixing layer depth and upper ocean heat content in SSTC + BGA are significantly different from the corresponding signals in SSTC + TDA (see in Figures 3c and 3d), although the corresponding EOF mode in both cases has a similar spatial pattern. This can be explained by the enhanced mixing efficiency with the Ekman pumping effect of TCs [Mei et al., 2013] in SSTC + BGA and the change of precipitation minus evaporation (PME) fluxes induced by these TC activities. The results suggest that maintaining correct TC statistics and their interactions with the large-scale flows can help improve the estimated climate signals by better representing the ocean subsurface heat content. Moreover, we expect that the climate prediction skill made by a high-resolution coupled model can be optimized through an appropriate high-resolution coupled data assimilation approach. While corrected TC activities generate more accurate ocean heat content initial conditions which are important for the TC intensity forecast [Lin et al., 2013], they also allow the prediction model to maintain the interaction of tropical storms and climate states thus reducing the forecasting errors at the early period of the prediction. The 2–3 year spin-up of tropical storm statistics in SSTC + BGA (shown in Figure 2) represents the time scale of the subsurface ocean responding to the TC-induced Ekman pumping and PME fluxes so as to modulate SSTs. Thus, we may expect that the correct TC statistics in climate estimation can improve the climate prediction skill within this time scale. This would be an interesting research topic in follow-up studies.

Summary and Discussions

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methodology
  5. Results
  6. Summary and Discussions
  7. Acknowledgments
  8. References

Due to incomplete understanding on physical processes and imperfect numerical implementation, a high-resolution climate model tends to produce significantly different tropical cyclone (TC) climatology and variability from the real world [Gualdi et al., 2008; Zhao et al., 2009; H.-S. Kim et al., submitted manuscript, 2013]. One usually corrects the model simulation by assimilating observed values such as atmospheric/oceanic temperature, winds, and salinity into a coupled model [Zhang et al., 2007; Sugiura et al., 2008]. However, due to the limitation of representation of observations and covariance model used in data assimilation, a traditional scheme that preferably projects observations to correct large-scale background tends to filter out small-scale cyclones. A background adjustment (BGA) scheme is designed to separately process the large-scale background and the small-scale perturbations for reconstructing historical cyclone statistics in a cyclone-permitting model. By maintaining the interactions between small-scale perturbations and successively corrected large-scale background, the BGA scheme can successfully retrieve the observed cyclone statistics that in return improve estimated ocean states. The improved ocean initial conditions together with the continuous interactions of cyclones and background flows are expected to reduce model forecast errors.

When more types of higher-resolution data such as radar and satellite measurements are incorporated into a high-resolution climate model [Zhang et al., 2011], the BGA scheme that separately processes the large-scale background and the small-scale perturbations can be refined by appropriately processing small-scale perturbations to reconstruct the structure of individual TCs. Such high-resolution model initialization procedure with progressively advanced models can advance seamless weather-climate predictions when more continuous interactions between TCs and climate signals are expected to enhance the model predictability.

Acknowledgments

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methodology
  5. Results
  6. Summary and Discussions
  7. Acknowledgments
  8. References

Authors would like to express their special thanks to Tony Rosati and Tom Delworth for their persistent guidance and encouragement on the efforts to improve the GFDL ECDA system for climate predictability studies. Thanks also go to G. Vecchi, Tom Knutson, and Isaac Held at GFDL for their generous discussions during the research. Thanks go to Larry W Horowitz and Jan-Huey Chen for their helps on the NCEP/NCAR data. Thanks also go to Tim Marchok and Lucas Harris at GFDL as well as two anonymous reviewers for their helpful comments on a preliminary version of this paper.

The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methodology
  5. Results
  6. Summary and Discussions
  7. Acknowledgments
  8. References