Volume 125, Issue 1 e2019JD031304
Research Article
Open Access

Data Assimilation for Climate Research: Model Parameter Estimation of Large-Scale Condensation Scheme

Shunji Kotsuki

Corresponding Author

Shunji Kotsuki

RIKEN Center for Computational Science, Kobe, Japan

Center for Center for Environmental Remote Sensing, Chiba University, Chiba, Japan

PRESTO, Japan Science and Technology Agency, Chiba, Japan

RIKEN interdisciplinary Theoretical and Mathematical Sciences Program, Kobe, Japan

RIKEN Cluster for Pioneering Research, Kobe, Japan

Correspondence to: S. Kotsuki,

[email protected]

Contribution: Conceptualization, Methodology, Validation, Formal analysis, ​Investigation, Data curation, Writing - original draft, Writing - review & editing, Visualization, Funding acquisition

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Yousuke Sato

Yousuke Sato

Department of Earth and Planetary Sciences, Faculty of Science, Hokkaido University, Sapporo, Japan

RIKEN Center for Computational Science, Kobe, Japan

Contribution: Conceptualization, Methodology, Software, ​Investigation, Writing - review & editing, Funding acquisition

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Takemasa Miyoshi

Takemasa Miyoshi

RIKEN Center for Computational Science, Kobe, Japan

RIKEN interdisciplinary Theoretical and Mathematical Sciences Program, Kobe, Japan

RIKEN Cluster for Pioneering Research, Kobe, Japan

Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan

Department of Atmospheric and Oceanic Science, University of Maryland, College Park, MD, USA

Contribution: Conceptualization, ​Investigation, Resources, Writing - review & editing, Supervision, Project administration, Funding acquisition

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First published: 03 January 2020
Citations: 10

Abstract

This study proposes using data assimilation (DA) for climate research as a tool for optimizing model parameters objectively. Mitigating radiation bias is very important for climate change assessments with general circulation models. With the Nonhydrostatic ICosahedral Atmospheric Model (NICAM), this study estimated an autoconversion parameter in a large-scale condensation scheme. We investigated two approaches to reducing radiation bias: examining useful satellite observations for parameter estimation and exploring the advantages of estimating spatially varying parameters. The parameter estimation accelerated autoconversion speed when we used liquid water path, outgoing longwave radiation, or outgoing shortwave radiation (OSR). Accelerated autoconversion reduced clouds and mitigated overestimated OSR bias of the NICAM. An ensemble-based DA with horizontal localization can estimate spatially varying parameters. When liquid water path was used, the local parameter estimation resulted in better cloud representations and improved OSR bias in regions where shallow clouds are dominant.

Key Points

  • This study proposes using data assimilation for climate research as a tool for optimizing model parameters objectively
  • When liquid water path or outgoing radiation was used, parameter estimation reduced clouds and mitigated radiation biases of a GCM
  • Estimating spatially varying parameters was beneficial for improving cloud representations in regions where shallow clouds are dominant

1 Introduction

Cloud plays important roles in the climate system through the radiation processes and hydrological cycle of the Earth (Trenberth et al., 2009). Therefore, cloud must be simulated appropriately in general circulation models (GCMs) for climate change assessments. However, despite its important roles in the climate system, cloud has not been simulated accurately, and it remains one of the greatest factors of uncertainty in climate predictions, as reported by the Fifth Intergovernmental Panel on Climate Change (IPCC AR5: Stocker et al., 2013). This has prompted a number of scientific efforts to reduce uncertainties in climate predictions due to cloud.

Satellite sensors provide valuable observation data to validate cloud representations in GCMs. From the late 1990s to 2000s, passive sensors on polar-orbiting and geostationary satellites have been widely used to evaluate cloud properties in GCMs (e.g., Quaas & Boucher, 2005; Quaas et al., 2006; Rotstayn & Liu, 2003; Suzuki et al., 2004). Since the launch of CloudSAT in 2006, it has been possible to assess the growth process of cloud particles, as well as the cloud properties themselves, through joint observation by the active sensor on CloudSAT and passive sensors on other satellites included in the A-train constellation (Nakajima et al., 2010a; Nakajima et al., 2010b; Suzuki et al., 2010). This joint observation enables so-called “process-oriented” validation to evaluate the growth processes of cloud particles (e.g., Tsushima et al., 2017; Thomas et al., 2019).

This process-oriented validation has shown that autoconversion (i.e., large-scale condensation), defined as the conversion from clouds to rain, is a sensitive process for climate predictions (Golaz et al., 2013; Shiogama et al., 2012; Suzuki, Golaz, et al., 2013). Using a GCM, Golaz et al. (2013) investigated the sensitivity of climate simulations to a tuning parameter of autoconversion, the critical radius from rain to cloud. They reported that satellite observations did not support simulated cloud microphysics properties with a critical radius parameter tuned to reproduce historical temperature trends. This suggested that the GCMs have flawed representations of autoconversion. In addition to their GCM, Jing et al. (2017) reported large intermodel variability of the autoconversion process among several global-scale models. These studies suggested that the determination of reasonable parameters for autoconversion play an important role in climate prediction. The tuning parameters have been determined empirically. However, determining reasonable parameters for GCMs remains challenging.

Data assimilation (DA) provides a mathematical algorithm to optimize parameters objectively in numerical weather prediction (NWP) models instead of manual tuning. Parameter estimations for NWP models have been investigated mainly within theoretical frameworks by observing system simulation experiments in which the true parameters are known (e.g., Aksoy et al., 2006; Annan, 2005; Kang et al., 2011; Koyama & Watanabe, 2010; Ruiz et al., 2013a, 2013b; Ruiz & Pulido, 2015). Recent studies demonstrated that DA-based parameter estimations are beneficial even for real atmospheric forecasts (Schirber et al., 2013). For example, Kotsuki et al. (2018; hereafter K18) estimated an autoconversion scheme parameter and improved 5-day precipitation forecasts, especially for weak rain, using a global atmospheric model aka the Nonhydrostatic ICosahedral Atmospheric Model (NICAM; Tomita & Satoh, 2004; Satoh et al., 2008, 2014). However, K18 also reported that the estimated parameter for the optimal fit to precipitation data degraded outgoing longwave radiation (OLR). This implies that optimal parameters for medium-range-scale NWP can contradict optimal parameters for climate-scale predictions, perhaps due to imperfections in the model and observation data. In addition, cloud parameterization itself has some room for improvement. For instance, cloud parameterization and its tuning parameters have been determined empirically with limited field observations. Also, these empirical parameters are usually set as uniform values globally even though cloud characteristics vary region to region.

This study aims at investigating whether DA can contribute to climate studies as a tool for model parameter estimation. The adjustment of radiation bias plays a crucial role in climate-scale simulations. Here, we extend the previous study by K18 and explore means of mitigating radiation bias through model parameter estimation with DA. We use the NICAM-based DA system, which incorporates the Local Ensemble Transform Kalman Filter (LETKF; Hunt et al., 2007) as the DA component. In addition to the medium-range-scale NWP, NICAM has also been used for climate-scale simulations (Kikuchi et al., 2017; Kodama et al., 2015). We use the NICAM-LETKF system, which can estimate model parameters together with model state updates (K18). The first question is whether DA can be used to estimate a model parameter for mitigating radiation bias. If DA works, then the second question is what observations are useful for mitigating radiation bias. We select a parameter in the autoconversion scheme (i.e., Berry's parameterization; Berry, 1967) and estimate the parameter using four different satellite observations: liquid water path, outgoing shortwave radiation (OSR), OLR, and precipitation. We perform four parameter estimation experiments using each of the four observation types separately.

Model parameters are usually assumed to be globally constant. However, the optimal parameter may be spatially different in terms of the autoconversion scheme. The cloud type and cloud thickness are different from region to region based on atmospheric stability (i.e., lower tropospheric stability [LTS]), as discussed in several previous studies (e.g., Kawai et al., 2015; Koshiro & Shiotani, 2014; Matsui, 2004; Matsui et al., 2006). The globally uniform parameter cannot reflect the dependence of the conversion speed on the cloud type and cloud geometrical thickness. Therefore, our third question is whether spatially varying model parameters are beneficial to reduce atmospheric radiation errors.

This paper is organized as follows. Section 2 provides the methodology. Section 8 describes the experimental settings. The results are presented and discussed in section 9. Finally, section 12 provides a summary.

2 Methodology

2.1 NICAM-LETKF System

In this study, simultaneous estimations of model states and parameters are performed using the NICAM-LETKF system (Terasaki et al., 2015, 2019; Kotsuki, Kurosawa, & Miyoshi, 2019) incorporating the NICAM as a GCM component and LETKF as a DA component (cf. Figure 1 of K18). We use the NICAM at 112-km horizontal resolution with 38 vertical layers up to about 40 km. The Berry's parameterization (Berry, 1967) and prognostic Arakawa and Schubert scheme (Arakawa & Schubert, 1974) are employed for LSC and cumulus parameterization schemes, respectively.

Details are in the caption following the image
Time series of estimated B1 for liquid water path (LWP)-Global (blue), outgoing longwave radiation (OLR)-Global (green), outgoing shortwave radiation (OSR)-Global (red), and Global Satellite Mapping of Precipitation (GSMaP)-Global (magenta) experiments. The abscissa shows months and years.
The LETKF is an efficient upgrade of the Ensemble Transform Kalman filter (ETKF; Bishop et al., 2001). The model state estimates are always performed by the LETKF. For parameter estimations, the ETKF is used for global parameter estimation, and the LETKF is used for local parameter estimation. The analysis equations of the ETKF are given by
urn:x-wiley:2169897X:media:jgrd55961:jgrd55961-math-0001(1)
urn:x-wiley:2169897X:media:jgrd55961:jgrd55961-math-0002(2)
urn:x-wiley:2169897X:media:jgrd55961:jgrd55961-math-0003(3)

Here, m is the ensemble size, X is the ensemble state matrix (Rn × m), δX is the ensemble perturbation matrix (Rn × m), H is the linear observation operator (Rp × n), I is the identity matrix, R is the observation error covariance (Rp × p), and urn:x-wiley:2169897X:media:jgrd55961:jgrd55961-math-0004 is the analysis error covariance in the ensemble space (Rm × m), where p and n are the numbers of observations and the model state variables, respectively. The superscripts o, b, and a, denote observation, background (prior), and analysis (posterior), respectively. Tilde indicates the ensemble space that is spanned by the background ensemble perturbation matrix δXb. The model-space background and analysis error covariance are represented by urn:x-wiley:2169897X:media:jgrd55961:jgrd55961-math-0005 and urn:x-wiley:2169897X:media:jgrd55961:jgrd55961-math-0006. In the ensemble space, the background error covariance urn:x-wiley:2169897X:media:jgrd55961:jgrd55961-math-0007 is the identity matrix. Equations 1 and 2 correspond to ensemble mean and perturbation updates, respectively. The ETKF solves the update equations, equations 13, only once by assimilating global observations. In contrast to the ETKF, the LETKF solves the update equations at every model grid point by assimilating local observations within the localization influence radius.

Practical EnKF applications for large dimensional systems require localization to remove erroneous covariance due to insufficient ensemble size. The localization of the LETKF is realized in the observation space. The observation error covariance R is inflated in equations 1 and 3 such that the distant observations have less impact (Brankart et al., 2003; Hunt et al., 2007; Miyoshi & Yamane, 2007).

2.2 Parameter Estimation

This study focuses on the parameters of the autoconversion process due to its high sensitivity to the climate (Golaz et al., 2013; Shiogama et al., 2012; Suzuki, Golaz, et al., 2013; Suzuki, Stephens, et al., 2013). Here, we use Berry's LSC scheme to represent the autoconversion process, which is given by
urn:x-wiley:2169897X:media:jgrd55961:jgrd55961-math-0008(4)
where P is the autoconversion rate (s−1), l is the cloud water mixing ratio (kg/kg), ρ is the air density (kg/m3), and Nc is the total number of cloud droplets (m−3), respectively (cf. Takemura et al., 2005). Berry's parameterization includes three tunable parameters B1, B2, and B3, whose default settings are 0.10 (B1,default, m3/kg), 0.12 (s), and 1.0×10−12 (s/kg), respectively, in NICAM. This study estimates only the B1 parameter; its definition range is bounded by [0,1].

The model parameter estimation is performed by ETKF (LETKF). In EnKF-based model parameter estimation, ensemble NICAM forecasts are performed under conditions where each ensemble member has a different parameter. In the DA step, the parameter ensemble is updated by applying equations 1 and 2 to the model parameter ensemble matrix Xparam, where subscript param denotes the parameters to be estimated. In the case of global parameter estimation by ETKF, the model parameter ensemble is a vector (R1 × m), while the model parameter ensemble is a matrix ( urn:x-wiley:2169897X:media:jgrd55961:jgrd55961-math-0009) in the case of local parameter estimation where nh is the number of horizontal model grid points. In K18's algorithm, the parameter estimation is separated from the model state estimation (cf. Figure 1 of K18). With this separation, we can apply a different localization scale for the model parameter estimation from that for the model state estimation. The assimilation order of model and parameter estimations has no impact on their analyses. Mathematically, this system is equivalent to the simultaneous estimation of model states and parameters (aka augmented state approach) with different localization scales. Subsequent ensemble NICAM forecasts will be performed with the updated ensemble parameters.

The global parameter estimation with ETKF is mathematically equivalent to the LETKF with the infinite localization scale. For local parameter estimation, a larger localization scale results in spatially smoother parameter fields. This study investigates the sensitivity of the localization scale to estimated parameter patterns (cf. section 10). No vertical localization is considered. That is, model parameters vary in space only horizontally, not vertically. Parameter ensemble spread is a tunable parameter that corresponds to time-smoothing strength (cf. Figure 4 of K18). Smaller parameter spread results in less temporal fluctuation and requires a longer period for spin-up. K18 indicated that estimated parameters were insensitive to the parameter spread with a sufficient spin-up period. Following K18, we set the parameter spread to be B1,spread=0.05.

Following K18, two treatments are applied for the model parameter estimation. Due to the assumption of normal error distribution with infinite tails, the EnKF could generate parameters beyond their definition ranges. To avoid this, we apply a hyperbolic tangent-based function for model parameter estimations (cf. Figure 2 of K18), which is given by
urn:x-wiley:2169897X:media:jgrd55961:jgrd55961-math-0010(5)
where Xparam represents parameters estimated by DA and Φ(Xparam) shows parameters used in NICAM forecasts, respectively. The superscripts i and k demote the ith horizontal model grid point and the kth ensemble member. The subscripts min and max denote the minimum and maximum values of the parameter range of B1 (cf. B1,min = 0 and B1,max = 1). The ETKF (LETKF) model parameter estimations are conducted for Xparam by assuming that Xparam follows a Gaussian error distribution. Subsequent NICAM ensemble forecasts are performed with the transformed parameter Φ(Xparam). In addition, a relaxation to prior spread method (RTPS; Whitaker & Hamill, 2012) is used to maintain the ensemble spread. In contrast to the model state variables, the model parameter ensemble Xparam never changes during forecasts. Namely, the ensemble spread (i.e., uncertainty) of the model parameters never increases by ensemble forecasts. Therefore, maintaining the ensemble spread is very important for ensemble-based model parameter estimations (Ruiz et al., 2013b). Here we use RTPS with relaxation parameter 1.0 so that the analysis spread is the same as the background spread. Namely, we keep the prescribed ensemble spread B1,spread over the experimental period.
Details are in the caption following the image
Global patterns of the time-mean liquid water path (LWP; g/m2) for (a) CTRL, (b) LWP-Global, (c) outgoing longwave radiation (OLR)-Global, (d) outgoing shortwave radiation (OSR)-Global, (e) Global Satellite Mapping of Precipitation (GSMaP)-Global, and (f) Advanced Microwave Scanning Radiometer 2 (AMSR2) observations, averaged over 12 months from January to December 2015. The gray color in (f) means no observation data.

2.3 Observation Data

Here, we describe observation data used for model state updates and parameter estimations. K18 separated algorithms for model state and parameter updates (cf. Figure 1 of K18). Therefore, observation data for parameter estimations can be different from those for the model state updates.

2.3.1 Observation Data for Model State Estimations

For model state updates, we assimilate typical observations used in NICAM-LETKF: satellite radiances of the Advanced Microwave Sounding Unit-A (AMSU-A), the gauge-calibrated version of the Global Satellite Mapping of Precipitation (aka GSMaP_Gauge; Kubota et al., 2007, Ushio et al., 2009), and conventional observation from the National Centers for Environmental Prediction (NCEP; aka NCEP PREPBUFR). See Terasaki et al. (2015), Terasaki and Miyoshi (2017), and Kotsuki, Miyoshi, et al. (2017) for details regarding how PREPBUFR, AMSU-A radiance, and GSMaP_Gauge data are assimilated in the NICAM-LETKF. The NICAM-LETKF assimilates these observations and updates atmospheric states every 6 hr.

2.3.2 Observation Data for Parameter Estimations

Four satellite observation datasets are used for the parameter estimation experiments (Table 1). This study aims at exploring useful observations for mitigating radiation bias. Therefore, we perform four parameter estimation experiments using the four observation types separately. We do not perform an experiment using more than one observation datasets simultaneously to clarify the impact from each observation type separately.

Table 1. Observation Data Used for Parameter Estimation Experiments
Observation DA frequency Assimilated variable Observation error SD
LWP 6 hourly LWP 60 (g/m2)
OLR 6 hourly OLR 33.1 (W/m2)
OSR 6 hourly albedo = OSR/ISR (if ISR ≥ 50 W/m2) 0.14 (−)
GSMaP 6 hourly log-transformed precipitation min (0.01, 0.5×yo′)
  • Abbreviations: DA: data assimilation; GSMaP: Global Satellite Mapping of Precipitation; ISR: incoming shortwave radiation; LWP: liquid water path; OLR: outgoing longwave radiation; SD: standard deviation.
Table 2. List of Experiments
Name of experiment Parameter estimation Section
DA method Parameter spread Observation Localization scale
CTRL / / / / 4.1, 4.2
LWP-Global ETKF 0.05 LWP 4.1, 4.2
OLR-Global ETKF 0.05 OLR 4.1
OSR-Global ETKF 0.05 OSR 4.1
GSMaP-Global ETKF 0.05 GSMaP 4.1
LWP-L400lm LETKF 0.05 LWP 400 km 4.2
LWP-L200km LETKF 0.05 LWP 200 km 4.2
LWP-L100km LETKF 0.05 LWP 100 km 4.2
  • Abbreviations: DA: data assimilation; ETKF: Ensemble Transform Kalman Filter; GSMaP: Global Satellite Mapping of Precipitation; LETKF: Local Ensemble Transform Kalman Filter; LWP: liquid water path; OLR: outgoing longwave radiation; OSR: outgoing shortwave radiation.

The first observation is the liquid water path (LWP; g/m2) retrieved from observations by the Advanced Microwave Scanning Radiometer 2 (AMSR2) instrument on the Global Change Observation Mission-Water (GCOM-W) satellite. The GCOM-W is on a Sun-synchronous orbit as a part of the A-train satellite constellation and crosses the equator each day at around 1:30 p.m. of local time. We use AMSR2-based LWP data version 2 2.210.210. The observation error standard deviation (SD) is set at 60 g/m2 following Chen et al. (2015).

The second and third observations are OLR (W/m2) and OSR (W/m2). This study uses OLR and OSR data provided by Clouds and the Earth's Radiant Energy System (CERES; Wielicki et al., 1996), known to be among the most accurate radiation data regarding the Earth's radiation budgets. Here, we use the CERES data version SYN1deg-3Hour Edition4. OLR and OSR data are retrieved with multiple sensors, including the MODerate resolution Imaging Spectroradiometer (MODIS) on Terra and Aqua satellites, and visible and infrared imagers on geostationary satellites. The OSR value is closely linked to latitude-dependent incoming shortwave radiation. In this study, OSR data are assimilated as the normalized variable, that is, albedo (= OSR/incoming shortwave radiation). While albedo is not a Gaussian-distributed variable, the ETKF can analyze the parameters based on the minimum variance estimate of the Kalman filter. Here we assimilate albedo only for model parameter updates. Since OSR and albedo are diagnostic (i.e., nonprognostic) variables, assimilations of albedo do not affect atmospheric states in DA steps. Assimilations of albedo affect the B1 parameter and eventually affect atmospheric state via forecast.

There have been no previous studies using OLR and OSR data for DA. In addition to the measurement error, observation operator and representativity errors need to be considered in DA (Fielding & Stiller, 2019). This study diagnosed the observation error SDs for OLR and OSR prior to the parameter estimation experiments. For that purpose, we performed a preliminary DA cycle experiment for 2 months (CTRL in section 8). With the second month results of the DA cycle experiment, we estimated the observation error SDs for OLR and OSR with the Desroziers et al. (2005)'s innovation statistics given by
urn:x-wiley:2169897X:media:jgrd55961:jgrd55961-math-0011(6)
where <●> denotes the statistical expectation and σb and σo are the background and observation error SDs, respectively. Since equation 6 has two unknown parameters σb and σo, an additional assumption is needed to estimate σb. The observation and background error SDs have generally similar amplitudes. For example, σb/σo averaged for all assimilated observations was diagnosed to be 0.70 in the NICAM-LETKF in our ongoing study. With the assumption of σb = 0.70 × σo, the observation error SDs for OSR and OLR were estimated to be 0.14 and 33.1 (W/m2), respectively. Although the error estimates for the satellite products are not available, these values are similar to globally averaged SDs of natural variability for OSR and OLR in the diagnosed period (0.10 and 24.9 W/m2).

The fourth observation is GSMaP_Gauge (hereafter referred to as GSMaP). Following K18, the logarithmic-transformed GSMaP (yo '  = ln(yo+α)) is assimilated to update model parameters, where α is set to be 0.6 (mm/6 hr). Larger observation error SD is used for intense precipitation (Table 1) as typically conducted in precipitation DA (e.g., Lien et al., 2013, 2016). Although we already know that estimating B1 by assimilating GSMaP degrades radiation budgets, we repeat the same experiment for comparison with other parameter estimation experiments.

The original LWP, OSR, OLR, and GSMaP data are aggregated into the NICAM model grid points such that each observation corresponds to one model grid point. This aggregation aims to match the spatial scale of atmospheric phenomena for forecasts and observations. The observation error of GSMaP data is known to be spatially correlated (Kotsuki, Miyoshi, et al., 2017). Therefore, we assimilate GSMaP data at every 5 × 5 horizontal model grid points (approximately 750–800 observations per DA cycle). No observation thinning is applied to LWP, OSR, and OLR data.

3 Experimental Settings

First, we describe the experimental settings of a baseline control experiment (hereafter CTRL) without parameter estimation. The DA cycling interval is 6 hr. The ensemble size is 40, and vertical localization scales are 400 (km) and 0.4 (natural-log-pressure), respectively. Covariance inflation is employed by RTPS with a relaxation parameter of 0.90 (Kotsuki, Ota, et al., 2017). This experimental setting has been widely used for NICAM-LETKF experiments (e.g., Kotsuki, Kurosawa, & Miyoshi, 2019; Kotsuki, Kurosawa, Otsuka, et al., 2019; Kotsuki, Terasaki, et al., 2019).

Section 9 presents four parameter estimation experiments by assimilating LWP, OLR, OSR, and GSMaP, respectively. The B1 is assumed to be globally constant in section 9. Hereafter, these four experiments are referred to as LWP-Global, OLR-Global, OSR-Global, and GSMaP-Global, respectively.

Section 10 discusses the impacts of local parameter estimation. We performed three experiments with horizontal localization scales of 400, 200, and 100 km, referred to as LWP-L400km, LWP-L200km, and LWP-L100km, respectively. Here, we assimilate LWP for local parameter estimations.

We performed the experiments over 19 months from 0000 UTC 1 June to 1800 UTC 31 December 2015. The initial model-state ensemble was obtained from the long-term NICAM-LETKF experiments (Terasaki et al., 2019). We generated the initial parameter ensemble by independent random numbers from a Normal distribution whose mean B1,default and SD B1,spread are 0.10 and 0.05, respectively (cf. section 3). The experimental results are verified with observed LWP, OLR, and OSR. We also verify atmospheric variables against the ERA interim reanalysis (Dee et al., 2011). More satellite observations are assimilated in the ERA interim reanalysis than in the NICAM-LETKF. Therefore, it is reasonable to validate the NICAM-LETKF results against the ERA interim reanalysis.

4 Results and Discussion

4.1 Global Parameter Estimation

Figure 1 shows the time series of estimated B1 with four different observations: LWP, OLR, OSR, and GSMaP. With GSMaP, the estimated parameter decreased rapidly in the first month, as in K18. This would be caused by the bias in precipitation between NICAM and GSMaP. Although the estimated B1 reduced the precipitation bias relative to GSMaP, the NICAM's overestimation bias in precipitation was not removed completely (cf. Figure 6a of K18). In the GSMaP-Global experiment, the parameter estimation reduced the precipitation bias only by regulating B1. For further improvement, it would be necessary to estimate other relevant parameters such as the ones in cumulus parameterization schemes. Miyakawa et al. (2018) showed that the parameters in a cumulus parameterization scheme were sensitive to precipitation bias in NICAM.

In contrast, the other three experiments showed increases in estimated B1. With OSR and OLR, the estimated parameter reached about 1.0. OSR-Global showed a more rapid increase in estimated B1 than OLR-Global because CTRL has a larger bias in OSR than in OLR (cf. Figure 3). DA estimates B1 to mitigate the bias in CTRL, and a larger bias results in more rapid change of B1. With LWP, the estimated parameter increased in the first month, showing temporal fluctuations between 0.4 and 0.7. No clear seasonality was seen in global parameter estimations in any of the experiments.

Details are in the caption following the image
Global-mean radiation biases (W/m2) relative to the Clouds and the Earth's Radiant Energy System (CERES) data for CTRL, liquid water path (LWP)-Global, outgoing longwave radiation (OLR)-Global, outgoing shortwave radiation (OSR)-Global, and Global Satellite Mapping of Precipitation (GSMaP)-Global experiments, averaged over 12 months from January to December 2015. The cyan and orange bars denote biases for OLR and OSR, respectively. The abscissa shows the names of experiments.
Details are in the caption following the image
Global-mean temperature biases (K) relative to the ERA-Interim reanalysis (Nonhydrostatic ICosahedral Atmospheric Model [NICAM] minus ERA-Interim) for the (a) Northern Hemisphere, (b) Tropics, and (c) Southern Hemisphere, averaged over 12 months from January to December 2015. The black, blue, green, and red lines show the CTRL, liquid water path (LWP)-Global, outgoing longwave radiation (OLR)-Global, and outgoing shortwave radiation (OSR)-Global experiments, respectively. The vertical axis shows the pressure level (hPa).
Details are in the caption following the image
Global-mean relative improvements (%) in background root-mean-square difference (RMSD) relative to the ERA-Interim reanalysis for (a) zonal wind (m/s), (b) meridional wind (m/s), and (c) temperature (K), averaged over 12 months from January to December 2015. The blue, green, and red lines show the liquid water path (LWP)-Global, outgoing longwave radiation (OLR)-Global, and outgoing shortwave radiation (OSR)-Global, respectively. A negative (positive) value indicates improvement (degradation) with reference to CTRL due to parameter estimation. The vertical axis shows the pressure level (hPa).
Details are in the caption following the image
Spatial patterns of locally-estimated B1, averaged over 12 months from January to December 2015 for (a) liquid water path (LWP)-L400km, (b) LWP-L200km, and (c) LWP-L100km experiments. The red and blue colors indicate increases and decreases from the default value (B1,default=0.10) due to parameter estimation.
Details are in the caption following the image
(a) Similar to Figure 6 b but with four rectangles used for computing domain-average parameters in panels (b1)−(b4). Panels (b1)–(b4) show the time series of estimated B1 parameters averaged over (b1) global (GLBL; 180°W−180°E and 60°S−60°N), (b2) Intertropical Convergence Zone (ITCZ; 160−100°W and 10°S−10°N), (b3) off the coast of California (USCA; 123−108°W and 15−25°N), and (b4) off the coast of Peru (PERU; 90−75°W and 25−12°S). The blue, purple, orange, and cyan lines are liquid water path (LWP)-Global, LWP-L400km, LWP-L200km, and LWP-L100km experiments, respectively. LWP-Global (blue line) shows the same value in four panels (b1)−(b4) because of the estimation as the globally-uniform parameter.
Details are in the caption following the image
Similar to Figure 2 but for (a) CTRL, (b) liquid water path (LWP)-Global, (c) LWP-L400km, (d) LWP-L200km, (e) LWP-L100km, and (f) AMSR2 observations.
Details are in the caption following the image
Similar to Figure 3 but for CTRL, liquid water path (LWP)-Global, LWP-L400km, LWP-L200km, and LWP-L100km experiments.
Details are in the caption following the image
Global patterns of the time-mean bias relative to Clouds and the Earth's Radiant Energy System (CERES) data for (a–c) outgoing short wave radiation (OSR; W/m2) and (d–f) outgoing long wave radiation (OLR; W/m2), averaged over 12 months from January to December 2015. Panels (a) and (d), (b) and (e), and (c) and (f) show CTRL, liquid water path (LWP)-Global, and LWP-L200km experiments, respectively. The warm (cold) color represents overestimated (underestimated) outgoing radiations relative to CERES data.

Figure 2 shows the global patterns of time-mean LWP. AMSR2 observations showed relatively large LWP (≥80 g/m2) in convergence regions, such as in storm track regions (30–50°N and 30–50°S) and the tropics. CTRL overestimated LWP over the ocean, suggesting that B1,default have slow autoconversion. GSMaP-Global markedly reduced the rate of autoconversion (B1 ≈ 0.0). Therefore, GSMaP-Global intensified the overproduced bias of LWP. LWP-Global, OLR-Global, and OSR-Global showed similar spatial patterns to AMSR2 observations. Due to the increased B1, cloud liquid water tended to be converted faster to raindrops in these three experiments. However, simulated LWP of OLR-Global and OSR-Global were smaller than AMSR2 observations. Among the four experiments, LWP-Global resulted in the most similar LWP to AMSR2 observations, as designed.

Figure 3 shows the global mean radiation biases for OLR and OSR relative to the CERES data. CTRL showed underestimated OLR and overestimated OSR. Overproduced clouds resulted in more reflection of incoming solar radiation, resulting in an overestimation of OSR. Therefore, the overestimated OSR in CTRL would be caused by the overestimated LWP (Figure 2a). With parameter estimations by assimilating LWP, OLR, and OSR, these biases in OLR and OSR were mitigated successfully. LWP-Global, OLR-Global, and OSR-Global resulted in increased B1, namely, faster conversion from cloud to rain, resulting in mitigation of cloud bias, which is closely linked to radiation bias. In contrast, the parameter estimation with GSMaP intensified radiation biases because of the intensification of overproduced clouds.

Here, we discuss why estimating B1 by assimilating GSMaP degraded the radiation bias. K18 showed that decreased (increased) B1 resulted in decreased (increased) precipitation (Figure 8 a of K18). In addition, decreased (increased) B1 led to slower (faster) autoconversion and resulted in more (less) LWP (Figure 2). These relations between B1-precipitation and B1-LWP can be explained by equation 4. When we estimated B1 by assimilating GSMaP, the model parameter was optimized to mitigate errors in falling precipitation amount. Since NICAM simulated more precipitation than GSMaP, the parameter estimation decreased B1 in GSMaP-Global. However, CTRL overestimated not only precipitation but LWP. Therefore, GSMaP-Global enhanced the overproduced bias in LWP. The Earth's radiation is more sensitive to clouds than to precipitation. Consequently, GSMaP-Global would have resulted in degraded radiation bias. In contrast, the model parameter regulated floating clouds when estimated with LWP. In this case, the model parameters estimated by assimilating LWP mitigated radiation bias.

Under the perfect model and perfect observation framework, estimating model parameters by assimilating a certain observation type generally improves the fit to other types of observation. However, the model is always imperfect for the real atmosphere. Under the imperfect model scenario, estimating model parameters by assimilating a certain observation type sometimes worsens the fit to other types of observations. In this study, CTRL overproduced both precipitation and LWP. GCMs are developed and tuned for their own purposes such as for NWP and climate simulations. Therefore, the issue, overproduced precipitation and LWP, would not be a common phenomenon of GCMs. With other condensation schemes, model parameter estimation with precipitation observations might be beneficial for radiation budgets. Also, it would be beneficial to estimate multiple model parameters to reduce errors in both falling precipitation and floating clouds at the same time, for example, by regulating surface evaporation and cumulus precipitation processes. However, estimating multiple parameters is difficult (Schirber et al., 2013) and should be investigated in a future research.

We explored changes in atmospheric variables for LWP-Global, OLR-Global, and OSR-Global that improved radiation bias. Figure 4 compares the time-mean bias in temperature for the Northern Hemisphere (NH, 20–90°N), Tropics (TR, 20°S–20°N), and Southern Hemisphere (SH, 20–90°S). Estimating B1 changed the temperature mainly for the lower and middle troposphere (1,000–600 hPa). CTRL showed lower temperature bias in the SH and NH for the troposphere (1,000–300 hPa). As increased B1 accelerated autoconversion, vapor and clouds remained for less time in the atmosphere. The decreased clouds reflected less incoming solar radiation, resulting in a heating effect in the lower troposphere for LWP-Global, OLR-Global, and OSR-Global. Consequently, the cold bias of CTRL in the lower troposphere in the SH and NH was mitigated by B1 parameter estimation by assimilating LWP, OLR, and OSR. In the TR, estimating B1 intensified warm bias in the lower troposphere (1,000–800 hPa) and mitigated cold bias in the middle troposphere (800–600 hPa). This mixed impact may be caused by regulations of only an autoconversion parameter B1 to reduce errors in LWP, OLR, and OSR. We expect that estimating the other tunable parameters B2 and B3 of the Berry's LSC scheme (equation 4) would not solve the mixed impact because estimating B2 and B3 would regulate only the autoconvesion rate and would result in a similar autoconversion rate as the one obtained by estimating only B1. This study chose B1 among the three parameters since B1 has been manually tuned for climate simulations (e.g., Shiogama et al., 2012; Suzuki, Stephens, et al., 2013). To solve the mixed impact, we may need to explore estimating uncertain parameters beyond the LSC scheme. Cumulus parameterization plays important role in GCMs to regulate clouds and OLD in TR (Miyakawa et al., 2018). In TR, estimating parameter(s) of the cumulus parameterization may be necessary to mitigate temperature bias without detrimental impacts.

Figure 5 shows the time-mean relative improvements of the first-guess root-mean-square differences relative to the ERA-Interim reanalysis. Here, the relative improvement (%) is defined by
urn:x-wiley:2169897X:media:jgrd55961:jgrd55961-math-0012(7)
where the subscript CTRL and TEST indicate CTRL and parameter estimation experiments, respectively. A negative value indicates improvement due to parameter estimation. We computed the relative improvements for zonal wind (U, m/s; Figure 5a), meridional wind (V, m/s; Figure 5b), and temperature (T, K; Figure 5c). Increased B1 improved U, V, and T in the middle troposphere (500–800 hPa), which are the most important variables for medium-range NWP. In contrast, the estimated parameters degraded U, V, and T near the surface (850–1,000 hPa). Compared to U and V, estimation of B1 had a greater impact on T, suggesting that altering B1 may affect T more directly than it affects U and V.

Among LWP-Global, OLR-Global, and OSR-Global, LWP-Global showed the smallest degradation impacts. The following section discusses the impacts of local parameter estimation using LWP for observation data.

4.2 Local Parameter Estimation

Figure 6 compares the locally estimated B1 for LWP-L400km, LWP-L200km, and LWP-L100km. All experiments showed general increases in estimated parameter from the default value of 0.1. As LWP observations are available only over the ocean, parameter shifts were seen mainly over the ocean. However, some inland regions near the ocean showed shifts in values due to LETKF, which assimilates observations within the localization influence radius. Due to the smaller localization radius, LWP-L100km resulted in the finest parameter patterns. LWP-200km and LWP-100km resulted in larger B1 in tropical convective regions such as the Intertropical Convergence Zone (ITCZ). In contrast, some regions showed decreases in parameters near the Caspian Sea, Greenland, and Antarctica. Decreased parameters were also seen in shallow convection regions, such as off the west coasts of Peru, California, and Angora in LWP-200km and LWP-100km. These three regions agreed well with regions where stratocumulus clouds are dominant (Hahn & Warren, 2007; Wood, 2012). In these regions, much effort has been made to solve the so-called “too few, too bright clouds” problem of GCMs (e.g., Nam et al., 2012).

Figures 7b1–7b4 show the time series of estimated B1 at different localization scales. The spin-up time increases as the localization scale becomes shorter because fewer observation data are assimilated with shorter localization scales. Among the four experiments, LWP-Global showed the greatest temporal fluctuation. In contrast, estimated parameters by LWP-100km and LWP-200km shifted smoothly during the experimental period. Again, the estimated parameter remained lower in shallow convection regions (Figures 7b3 and 7b4).

Although no seasonal changes were seen in the global parameter estimation, we observed seasonal parameter shifts in the local parameter estimations off the coasts of California (USCA) and Peru (PERU). In USCA, estimated B1 was relatively high in winter (November–January) and low in summer (June–August). In PERU, estimated B1 was relatively high at the end of summer (March–April). These seasonal patterns were similar to those of observed cloud top heights by cloud-aerosol lidar and infrared pathfinder satellite observation (CALIPSO; cf. Figure 8 of Kawai et al., 2015). Seasons with higher cloud tops (CALIPSO-based observations) corresponded to seasons with higher B1 (AMSR2's LWP-based parameter estimation). Again, the global parameter estimation could not address such seasonal patterns. Cloud top height becomes lower when the lower troposphere becomes more stable (cf. Figure 10 of Kawai et al., 2015), and the stable atmosphere leads to slower autoconversion. Therefore, LTS may be able to explain the spatial patterns of estimated B1. Developing an appropriate function to achieve spatially varying autoconversion parameterization using atmospheric variables (e.g., LTS) will be an important subject for future research to reduce the number of uncertain parameters in GCMs for climate predictions.

Figure 8 compares the LWP of five experiments with AMSR2 observation data. All parameter estimation experiments mitigated overproduced LWP bias. LWP-Global showed a good agreement with observations in the TR (Figure 8b) but underestimated LWP in the extratropical areas. Local parameter estimations increased LWP outside the tropics and resulted in better LWP patterns than did LWP-Global. LWP was increased in the extra tropics due to smaller B1, that is, slower autoconversion (Figure 6). The locally optimized B1 was beneficial in terms of reproducing the spatial patterns of observed LWP.

The local parameter estimations slightly degraded global radiation bias compared to the global parameter estimation (Figure 9). Figure 10 shows a comparison of the spatial patterns of bias of OSR and OLR for CTRL, LWP-Global, and LWP-L200km. CTRL showed significantly large OSR bias over the ocean (Figure 10a) because the overproduced clouds result in more reflection of incoming solar radiation. Estimating B1 by assimilating LWP data reduces clouds and mitigates OSR over the ocean (Figures 10b and 10c). However, OSR was still overestimated with the estimated parameter in LWP-Global and LWP-200km. In this study, the overestimated OSR bias could not be removed completely even with OSR-Global and OLR-Global in which estimated B1 were almost 1.0 (Figures 1 and 3). Therefore, larger B1 resulted in better radiation bias in OSR and OLR under the present experimental settings. Namely, it would be impossible to remove solar radiation bias by regulating only B1, and it would be necessary to estimate additional parameters, such as cumulus parameterization, to reduce the errors in OSR further. With such additional modifications, the local parameter estimation might outperform the global parameter estimation in terms of radiation budgets.

As pointed out, some inland regions near the ocean showed increases in B1 due to the assimilations of local observations (Figures 6a and 6b), while LWP observations are available only over the ocean. In contrast to the significant positive OSR bias over the ocean, opposite negative bias was also seen over land such as in Middle East, East China, Japan, and North America (Figure 10a). The increases in B1 were detrimental in these regions since increased B1 intensified negative bias of OSR through reductions of clouds. To obtain better parameter fields over land, it would be beneficial to use LWP observations valid over land such as the LWP retrieval from MODIS data.

LWP-Global showed underestimated OSR in some regions where shallow clouds are dominant (e.g., off the coasts of West Angora, Peru, and California). LWP-200km resulted in smaller B1 in these regions (Figures 6 and 7). Consequently, LWP-200km mitigated the bias underestimation for OSR compared to LWP-Global in shallow cloud regions. This suggests that local parameter estimation be beneficial to reduce radiation bias in such shallow cloud regions. In contrast, there was no significant difference in OLR between LWP-Global and LWP-200km (Figures 10e and 10f).

5 Summary

This study was performed to improve the radiation bias of a GCM with DA. We selected a parameter from the autoconversion scheme of Berry (1967) and investigated two approaches to reducing radiation bias: estimation of the model parameter for different satellite observations and exploration of the advantages of spatially varying parameters. Our conclusions based on a series of experiments with NICAM-LETKF can be summarized as follows:
  1. Using LWP, OLR, or OSR, the parameter estimation accelerated autoconversion speed compared to the default model setting. This mitigated overestimated OSR bias by reducing clouds with accelerated autoconversion. In contrast, overestimated OSR bias was intensified when GSMaP precipitation was used for parameter estimation. DA can be used to mitigate radiation bias if appropriate observations are selected for parameter estimation. In the case of NICAM-LETKF, LWP, OLR, and OSR were useful observations to reduce radiation bias.
  2. An EnKF with horizontal localization (i.e., LETKF) enabled estimation of spatially varying model parameter fields whose manual optimization by trial and error would be impractical. Smaller localization scales required a longer time for spin-up but resulted in spatially finer parameter fields. When LWP was used, the local parameter estimation reproduced observed LWP better than the global parameter estimation did. However, the local parameter estimation did not outperform the global parameter estimation in terms of global radiation bias for OSR and OLR.
  3. The local parameter estimation resulted in relatively slower autoconversion in regions where shallow clouds are dominant. In addition, the local parameter estimation resulted in reasonable seasonalities of autoconversion off the coasts of California and Peru, as observed by CALIPSO. The local parameter estimation improved OSR bias in the shallow cloud regions. These promising results prompted us to develop a new parameterization to achieve spatially varying autoconversion in future studies.

With regard to climate-scale simulations, a great deal of research has aimed to tune model parameters to reduce radiation bias. B1 is a commonly used parameter to regulate the amount of cloud and changes in radiation budgets (e.g., Shiogama et al., 2012). This study successfully mitigated radiation bias by estimating B1 by assimilating OSR, OLR, or LWP data. Tuning of globally constant parameters can be performed manually, although it takes a long time and requires huge computational resources. However, manually tuning spatially varying parameters is practically infeasible. As demonstrated here, DA is a powerful tool for local optimization of model parameters.

When GSMaP was assimilated to estimate the parameter, radiation bias was worsened. The Earth's radiation is more sensitive to clouds than to precipitation. Therefore, it would be reasonable to use LWP, OSR, and OLR for parameter estimation for better radiation budget. Under the perfect model and observation scenario, estimating model parameters by assimilating a specific type of observation usually improves fit to other types of observations. However, this is not always the case due to imperfections in the model and observations. This is an important direction for future studies to explore means of estimating multiple model parameters and to improve both falling precipitation and floating clouds.

Acknowledgments

S. Kotsuki and Y. Sato developed the experimental system for the parameter estimation, conducted the experiments, and analyzed the results. T. Miyoshi is the PI and directed the research with substantial contribution to the development of this paper. The NICAM model code is available at http://www.nicam.jp/. The GSMaP precipitation data are available at http://sharaku.eorc.jaxa.jp/GSMaP/. The NCEP PREPBUFR data are available at http://rda.ucar.edu/datasets/ds337.0/. The CERES data are available at https://ceres.larc.nasa.gov/order_data.php. The GCOM-W/AMSR2 data are available at https://suzaku.eorc.jaxa.jp/GCOM_W/data/data_w_dpss.html. The LETKF code developed in this study is based on the open source code available at https://github.com/takemasa-miyoshi/letkf. All of the data used in this study are stored for 5 years in Chiba University. Due to the large volume of data and limited disk space, data will be shared online upon request ([email protected]). The authors thank the members of Data Assimilation Research Team, RIKEN Center for Computational Science (R-CCS) and JAXA's PMM project. This study was partly supported by JAXA Precipitation Measuring Mission (PMM); Advancement of meteorological and global environmental predictions utilizing observational “Big Data” of the social and scientific priority issues (Theme 4) to be tackled by using post K computer of the FLAGSHIP2020 Project of the Ministry of Education, Culture, Sports, Science and Technology Japan (MEXT); the Initiative for Excellent Young Researchers of MEXT; JST AIP grant number JPMJCR19U2; the Japan Society for the Promotion of Science (JSPS) KAKENHI grants JP15K17766, JP15K18128, and JP18H01549; and JST PREST MJPR1924. The study used the Supercomputer for earth Observation, Rockets, and Aeronautics (SORA) at JAXA, and the K computer provided by the RIKEN R-CCS (Project IDs: ra000015, hp150289, hp160229, hp170246, and hp180062).