## Abstract

When producing forecasts by integrating a numerical weather prediction model from an analysis, not all observations assimilated into the analysis improve the forecast. Therefore, the impact of particular observations on the forecast needs to be evaluated quantitatively to provide relevant information about the impact of the observing system. One way to assess the observation impact is to use an adjoint-based method that estimates the impact of each assimilated observation on reducing the error of the forecast. In this study, the Weather Research and Forecasting Model and its adjoint are used to evaluate the impact of several types of observations, including enhanced satellite-derived atmospheric motion vectors (AMVs) that were made available during observation campaigns for two typhoons: Sinlaku and Jangmi, which both formed in the western North Pacific during September 2008. Without the assimilation of enhanced AMV data, radiosonde observations and satellite radiances show the highest total observation impact on forecasts. When enhanced AMVs are included in the assimilation, the observation impact of AMVs is increased and the impact of radiances is decreased. The highest ratio of beneficial observations comes from GPS Precipitable Water (GPSPW) without the assimilation of enhanced AMVs. Most observations express a ratio of approximately 60%. Enhanced AMVs improve forecast fields when tracking the typhoon centers of Sinlaku and Jangmi. Both the model background and the analysis are improved by the continuous cycling of enhanced AMVs, with a greater reduction in forecast error along the background trajectory than the analysis trajectory. Thus, while the analysis–forecast system is improved by assimilating these observations, the total observation impact is smaller as a result of the improvement.

## 1. Introduction

In numerical weather prediction (NWP), an analysis can be produced through assimilation of observations into a “background” or first-guess state, often from a short forecast from the previous analysis. The updated analysis can then be used to continue the forecast–analysis cycle, as well as serve as initial conditions for a medium-range forecast. While the number and types of observations have increased, due largely to the growing availability of satellite data, the impact of those assimilated observations must be quantitatively evaluated to monitor the contribution to forecast skill.

One way to assess the observation impact on forecasts is through observing system experiments (OSEs; Masutani et al. 2010), whereby the evaluation of the observation impact is performed by comparing the forecast from a control analysis and the forecast from an analysis with specifically added or subtracted observations (e.g., Cardinali et al. 2007; Kelly et al. 2007; Yamaguchi et al. 2009; Jung et al. 2010, 2012; Yang et al. 2014). The observation impact on forecasts for specific atmospheric features or regimes can be evaluated by performing OSEs. For example, in the African Monsoon Multidisciplinary Analysis (AMMA) project, Agustí-Panareda et al. (2010) found that the assimilation of dropsonde observations enhanced easterlies in the Sahel region. Operational NWP centers perform OSEs when evaluating the performance of specific observation types or platforms on their operational model forecasts (e.g., Bouttier and Kelly 2001; Kelly et al. 2007; Lord et al. 2016). However, OSEs often require a significant amount of computer resources, making them less efficient when the goal is estimating the observation impact in NWP systems for numerous subsets of observations.

The calculation of observation sensitivity by an adjoint-based method can be a substitute for examining observation impacts by OSEs. By this method, each of the assimilated observations is provided an estimated impact on the forecast by assessing the forecast sensitivity to observations (FSO) from a single adjoint integration process. Because this method requires less computation time, the observation impact based on FSO is performed at most operational NWP centers (e.g., Gelaro and Zhu 2009; Cardinali 2009; Lorenc and Marriott 2014; Kim and Kim 2014), although the observation impact is a linear approximation based on the adjoint integration. The early concept of assessing observation impact by the adjoint method was introduced by Baker and Daley (2000). Langland and Baker (2004) used this technique to show that the observation impact of Advanced Television Infrared Observation Satellite Program (TIROS) Operational Vertical Sounder (ATOVS) was the largest among all observations types in the Southern Hemisphere for a short-range (24 h) forecast. Errico (2007) expanded the third-order approximation of the method that was used in Langland and Baker (2004). The observation sensitivity concepts in four-dimensional variational data assimilation (4DVAR) systems were further advanced by Daescu (2008), Lorenc and Marriott (2014), Joo et al. (2013), and Kim and Kim (2014).

There are benefits and drawbacks associated with the two observation impact estimation methods based on FSO and OSEs. Jung et al. (2013) showed that the observation impact based on the adjoint method is qualitatively consistent with that from OSEs for tropical cyclone (TC) forecasts in the western North Pacific during the 2008 typhoon season. Gelaro and Zhu (2009) found that calculating the observation impact by the adjoint method using a dry energy norm matches well with results from OSEs in temperate regions, and that the observation impact estimated from the adjoint method is often complementary but not entirely overlapping with that provided by OSEs because of the different strategies used in their formulation. Cardinali (2009) concluded that OSEs are advantageous to calculating the observation impact for long forecast lengths, while the adjoint method is more favorable for estimating the observation impact for shorter forecast lengths.

One observation type that consistently rates in the top tier of importance in terms of operational global model impacts is atmospheric motion vectors (AMVs). AMVs are routinely produced by many national satellite agencies from polar-orbiting or geostationary satellite imagery and can be obtained from the Global Telecommunications System (GTS). The estimates of wind speed and direction produced from the AMV process are derived from tracking the movements of cloud and water vapor features across several successive images using visible (VIS), infrared (IR), water vapor (WV), and shortwave IR (SWIR) channels. The height assignment of AMVs is determined in pressure coordinates from the target cloud-top temperatures and various semitransparent cloud correction routines, and then matched with collocated NWP profiles. Finally, the AMVs are subject to internal quality control procedures. Further details on AMV derivation and applications are available in Velden et al. (2005) and Deb et al. (2015).

There are many studies concerning the impact of assimilated AMVs on forecasts of TC track and intensity. Velden et al. (1998) and Goerss et al. (1998) showed a reduction in track errors for Atlantic hurricanes during the 1995 hurricane season when utilizing *Geostationary Operational Environmental Satellite-8* (*GOES-8*) AMV information in the U.S. Navy Operational Global Atmospheric Prediction System (NOGAPS) model. Wang et al. (2006) assimilated *Geostationary Meteorological Satellite-5* (*GMS-5*) information using 4DVAR for western North Pacific typhoon cases during 2002 and showed that typhoon track prediction errors were reduced by 10% when AMVs were assimilated. Deb et al. (2011) concluded that when AMVs from *Kalpana-1* were assimilated by three-dimensional variational data assimilation (3DVAR), the model track prediction errors of TC cases in the Indian Ocean were reduced by 10% for short-range (i.e., within 30 h) forecasts.

Operational satellite data-processing centers traditionally produce AMVs from imagery covering the full view of the geostationary satellite within their region. These “conventional AMV” datasets are normally accessed and assimilated by operational NWP centers worldwide. These “full disk” AMV datasets are usually tailored to capture the larger scales, and therefore the spatiotemporal sampling is more appropriate for global model analyses. Thus, prior to about 2011, most global AMV processing was routinely done at 3- or 6-h intervals.

This study examines the impact of conventional AMVs available from the GTS, plus another type of “enhanced” AMVs produced retrospectively for demonstration by the Cooperative Institute for Meteorological Satellite Studies (CIMSS) at the University of Wisconsin. These enhanced AMV datasets were derived for a selected period during tropical cyclone observation campaigns in the western North Pacific during September of 2008, and are defined by several attributes: 1) the datasets are produced at hourly rather than at 3–6-h intervals [1-h AMV; LeMarshall (1996)]; 2) the AMV processing algorithm utilizes rapid scan images when available (5–15-min update frequency vs normal 30 min), thereby improving the coherence in trackable features; 3) the targeting routines are set to achieve a higher density of AMVs over the selected areal domain; and 4) parameters of a postprocessing objective analysis and quality control process are adjusted to better represent smaller-scale flow fields as described in Velden et al. (1998). The 1-h AMVs have been shown to be important when analyzing TC steering flow tendencies, which can affect model forecast tracks (Berger et al. 2011). The rapid update of information can also help analyze the interaction between the TC outflow and the nearby shear environment, which can impact the intensity of the storm (Sears and Velden 2012, 2014). Wu et al. (2014) showed that the analysis and forecasting of track and intensity for Typhoon Sinlaku are much improved by assimilating enhanced AMVs produced by CIMSS with an ensemble Kalman filter and the Weather Research and Forecasting (WRF) Model. Wu et al. (2015) showed the effects of specific subsets of the enhanced AMVs on analyzed TC position, intensity, and structure by conducting data-denial OSEs, demonstrating that near-storm and upper-layer AMVs are important for improving the initial TC structure. Finally, Velden et al. (2017) tested the direct assimilation of enhanced AMV datasets in the Hurricane WRF Model (H-WRF) and found modest positive impacts on both track and intensity forecasts for selected Atlantic hurricane cases.

While there are numerous studies that show the impacts of AMVs on TC track and intensity prediction by using OSEs, there has been little research regarding the influence of AMVs on model forecast error reduction (FER) that comprehensively examines the impact of different observation types using FSO by the adjoint method, especially for forecast periods during TC events. Moreover, there is no relative comparison of the observation impact between conventional and enhanced AMV datasets obtained during special observation campaigns over specific time periods of TC activity.

Therefore, this study uses an adjoint-based observation impact method and OSEs to examine the impact of the enhanced AMVs on FER and TC forecasts, respectively. Experiments from selected TC events in the western North Pacific during 2008 are analyzed using the WRF Model, WRF Data Assimilation System (WRFDA), and the WRF adjoint model (WRFPLUS). From the calculations of FSO by the adjoint method (Auligné et al. 2011; Jung et al. 2013), observation impact, normalized observation impact, and the fraction of beneficial observations are evaluated. Section 2 presents the mathematical formulations for observation sensitivity and forecast error reduction, and section 3 provides details of the experiments. Section 4 presents the results of the experiments and section 5 provides a summary and discussion of the findings.

## 2. Mathematical formulation

### a. Forecast sensitivity to observations

The forecast state in NWP is derived from a nonlinear model and can be expressed as

where **x**^{0} and **x**^{f} are the initial conditions and the forecast, respectively, and are related to each other by the nonlinear model *N*. When calculating the forecast sensitivity by using the adjoint of the NWP model, one defines a response function *R* that represents some aspect of interest in the forecast state **x**^{f}, which can be represented by

The first-order variance of *R* (*δR*) is expressed as

In Eq. (3), is the tangent linear model, *δ***x**^{0} is a perturbation of the initial values, and the resulting forecast perturbation *δ***x**^{f} =*δ***x**^{0}. Because ^{T} is the adjoint model of , from the approximate equality between the second and the fourth terms in Eq. (3), the following relationship is satisfied:

Data assimilation (DA) is the process of finding the analysis state **x**_{a} (typically representing the initial condition **x**^{0}) by minimizing a cost function when a background state **x**_{b} and set of observations **y**^{0} are given. With the background error covariance , the observation error covariance , and the linear observation operator , optimal linear analysis is formulated by

where is the Kalman gain matrix that satisfies = (^{−1} + ^{T}^{−1})^{−1}^{T}^{−1}. Therefore, Eq. (3) can be written as

where **d** is the innovation vector that is equal to **y**^{0} − **x**_{b}. By forming the equality of the fourth and the fifth terms in Eq. (6), the sensitivity of *R* with respect to the observation (i.e., FSO) can be expressed as (Baker and Daley 2000)

According to Courtier (1997), is represented as

where is the matrix of analysis error covariance that corresponds to the inverse of the DA cost function’s Hessian matrix (Lorenc 1986; Kalnay 2003). Thus, the adjoint matrix of is expressed as

The adjoint-derived observation impact for any individual observation is defined as the product of the forecast sensitivity with respect to that observation and the observation innovation.

### b. Forecast error reduction

If the true state **x**_{t} of the atmosphere is known, the forecast error can be expressed as

where is the diagonal matrix that presents the weighting coefficients of the forecast error components. Here, , and *c*_{s} represent the Brunt–Väisälä frequency, potential temperature, density of the atmosphere, and speed of sound, respectively. In temporal climate regions, a dry energy norm can be used (Rabier et al. 1996; Zou et al. 1997; Palmer et al. 1998). The unknown true state of the atmosphere creates a problem when objectively evaluating the observation impact based on FER (Jung et al. 2013). However, the analysis state produced in the DA process is typically considered to be sufficiently close to the true state of the atmosphere to function as a reference state for computing FER. Therefore, this study uses the analysis state produced by WRF 3DVAR as the reference state.

The FER (Δ*e*) is the difference between the error norms of two forecasts (), which are integrated from the analysis (with DA, **x**_{a}) and background (without DA, **x**_{b}). The two forecast error norms (*e*_{a}, *e*_{b}) are expressed as

Combining Eqs. (6), (7), (10), and (11) produces the third-order approximation *δe*^{3} of nonlinear FER in Eq. (12):

where _{a} and _{b} are given trajectories’ resolvent matrices of tangent linear models and are expressed as ∂*N*(**x**_{a})/∂**x**_{a} and ∂*N*(**x**_{b})/∂**x**_{b}, respectively. The linear estimation of FER is used to estimate the observation impact. The augmented form of the third-order approximation *δe*^{3} is used in this study and is written as (Gelaro et al. 2007)

## 3. Experimental framework

### a. Model, data assimilation, and observations

The forecast model employed in this study is WRFv3.3, while the DA system is the 3DVAR system from WRFDA (Barker et al. 2012). The forecast model uses the Yonsei University (YSU) scheme (Hong et al. 2006) for planetary boundary layer parameterization, the Noah land surface model (Chen and Dudhia 2001) for land surface parameterization, the Kain–Fritsch scheme (Kain 2004) for cumulus parameterization, the WRF single-moment 6-class scheme (Hong and Lim 2006) for microphysical processes, the Dudhia scheme (Dudhia 1989) for shortwave parameterization, and the Rapid Radiative Transfer Model (RRTM) scheme (Mlawer et al. 1997) is used for longwave parameterization.

Except for enhanced AMVs, the observations that are assimilated in all experiments in this study are obtained from the National Center for Atmospheric Research (NCAR), which are used by the NCEP Global Data Assimilation System (GDAS) in Prepared Binary Universal Form for the Representation of Meteorological Data (PREPBUFR) format. The conventional AMVs, which are included in the NCAR dataset, are obtained by GTS. The enhanced AMV datasets used for this study were provided by CIMSS as part of The Observing System Research and Predictability Experiment (THORPEX) Pacific Asian Regional Campaign (T-PARC) and TC Structure-2008 (TCS-08) field campaigns. These AMVs were retrospectively produced using nominal 30-min images from the Multifunctional Transport Satellite (MTSAT), with datasets provided hourly (unlike conventional AMVs, which were available only every 6 h in 2008). All of the observation data assimilated in this study are summarized in Table 1.

### b. Experiments

The details for the three experiments that were performed in this study are shown in Table 2. All conventional observations except AMVs are assimilated in EXP0. In EXP1, all conventional observations but including the operational AMVs are used. Finally, all conventional data plus the 1-h AMVs are assimilated in EXP2. While EXP0 is the reference or control experiment, EXP1 is performed to examine the impact of conventional AMVs, and EXP2 is for determining the additional impact of the enhanced AMVs.

The experiments cover the period 0000 UTC 25 August 2008–1800 UTC 30 September 2008. The analyzed period for all experiments is all of September beginning with a 1-week spin-up process starting on 25 August. Figure 1 is the model spatial domain of the study, centered in the east Asia–western North Pacific region (25°N, 125°E), with 235 zonal grid points and 197 meridional grid points, and with a spatial resolution of 27 km between grid points. There are 41 vertical levels and the top of the model is at 50 hPa. Since this study uses the WRF regional model, lateral boundary conditions are necessary for every analysis cycle. The lateral boundary conditions are produced from NCEP Final Reanalysis (FNL), at 1° × 1° resolution, by the WRF Preprocessing System (WPS). At the very beginning of the spinup period, NCEP FNL data were used as the initial conditions for a cold start.

To produce the analysis state (which serves as the reference state for every analysis period), cycling was performed using the WRF 3DVAR data assimilation system. In EXP0, EXP1, and EXP2, NCAR observation data were assimilated every 0000, 0600, 1200, and 1800 UTC within a ±3-h assimilation window. In EXP2, DA for the additional enhanced (1 h) AMVs was performed every 0000, 0600, 1200, and 1800 UTC within a ±1.5-h assimilation window during all of September 2008.

Figure 2 shows the process of 6-h cycling for the three experiments and calculating the observation impact. Nonlinear FER is the difference in 24-h forecast error starting from two different states, which are formed with and without DA; thus, for all experiments the difference is defined between the 24-h forecast error and the 30-h forecast (which produces the background state 6 h into the integration, corresponding to the analysis state used to produce the 24-h forecast) error. In this study, we consider each EXP’s own analysis state as a reference state for validating forecasts since the primary focus is on measuring the impact of assimilating observations within its own cycle. If the same reference state is used for all three different experiments, then the FER and its associated observation impact can be affected by differences in observations as well as differences in analysis–forecast cycles of each experiment. Following Gelaro et al. (2010) and Lorenc and Marriott (2014), Eq. (10) is calculated vertically from the surface to 150 hPa in this study, so as not to consider large errors near the model top. Therefore, the forecast aspect (i.e., nonlinear FER) is defined from the surface to 150 hPa.

### c. Evaluation

To check the validity of the linearization of the adjoint model, nonlinear FER is compared with its linear estimation. The linear estimation of FER (i.e., linear FER or observation impact) is calculated by the 1-min interval forecast trajectory and backward integration of the adjoint model. In addition, the linear estimation of FER is calculated horizontally in the interior domain, excluding the three grid points nearest the lateral boundaries, so as not to consider spurious large sensitivities accumulated at the lateral boundaries after the adjoint model integration. To be consistent, the nonlinear FER is also evaluated for the same horizontal domain with the linear FER.

The observation impact is computed for each assimilated observation by the multiplication of the FSO and innovation vectors. The normalized observation impact is obtained by dividing the total observation impact of a given observation type or variable by the number of observations of that type or variable for every cycle. The fraction of beneficial observations is the ratio between the number of observations of a given type or variable that reduce the forecast error and the total number of observations. In all cases, a negative observation impact represents forecast improvement, since this indicates that assimilating an observation reduced forecast error relative to a forecast that was provided no DA on that cycle. Similar to the linear estimation of FER, all the quantities associated with the observation impact are calculated for the domain inside the lateral boundaries.

The center positions of the case study TCs for the analyses and 24-h forecasts are calculated by the YSU Tropical Cyclone Tracker (TCT; Kim and Kim 2010). These results are compared with the Regional Specialized Meteorological Center (RSMC) Tokyo best track to determine the TC forecast track errors. The distance between two center positions (km) is calculated by the method of Feser and Von Storch (2008), which is equivalent to

and

where *a* is the angle between the RSMC best track and the TC centers calculated from YSU TCT for each experiment; *d* is the distance between the TC centers of the best track and the experiments; *R*_{d} is the mean radius of the earth; φ_{1} and φ_{2} are the longitudes of the simulated and best track represented in radians, respectively; and Δφ denotes φ_{1} − φ_{2}. Likewise, Δλ is the difference in latitude between the simulated and best track in radians (λ_{1} − λ_{2}). In this study, the earth is assumed to be a perfect sphere with radius of 6371 km (Moritz 2000). The latitudinal, longitudinal, and distance errors of the TC centers from the three experiments for both analyses and 24-h forecasts were compared with RSMC best track every respective 6 h.

## 4. Results

### a. Forecast error reduction

Figures 3a–c represent the time series of 24-h nonlinear FERs and their linear estimates during September 2008 for every cycle in EXP0, EXP1, and EXP2, respectively. For nearly all periods, the values are negative, which implies that the forecast error is reduced overall with DA of the entire observational dataset. The time variations of nonlinear and linear FERs are similar with respect to time. Because the observation numbers vary for every analysis time period, nonlinear FERs at 0000 and 1200 UTC are larger than those at 0600 and 1800 UTC in EXP0, EXP1, and EXP2; this is most likely due to the availability of radiosonde observations at 0000 and 1200 UTC. Generally, the linear FER underestimates the nonlinear FER for all experiments. This is consistent with Jung et al. (2013), who used a different resolution and forecast length (6 h) but similar time and spatial domains as this study. As the forecast time increases, the adjoint calculation using the regional model causes large sensitivities at lateral boundaries, which is partially responsible for the overestimation of the linear FER (not shown). To avoid this boundary effect, in this study the FERs are calculated for the domain inside the lateral boundaries. The boundary effects on the adjoint-based observation impact estimation within a regional model framework need to be investigated, but that is beyond the scope of this study.

The average nonlinear FERs of EXP0 and EXP1 during September are −207.0 and −200.3 × 10^{5} J kg^{−1}, respectively, and the average linear FERs are −201.8 and −199.1 × 10^{5} J kg^{−1}, respectively. The differences between EXP0 and EXP1 in the mean error norm on the background trajectory, the mean error norm on the analysis trajectory, and mean FER are not statistically significant based on a two-sided Student’s *t* test at 95% confidence. When enhanced AMVs are assimilated in EXP2, the average nonlinear and linear FERs during September are −193.7 and −192.2 × 10^{5} J kg^{−1}, respectively, which demonstrates a smaller observation impact than that expressed in EXP0 or EXP1. On average, the 24-h forecast error (error on the analysis trajectory) in EXP2 is reduced by 3.4% relative to EXP0 and 1.3% relative to EXP1, and the 30-h forecast error (error on the background trajectory) in EXP2 is reduced by 3.9% relative to EXP0 and 1.7% relative to EXP1. While the forecast error is reduced on both the background trajectory and the analysis trajectory in EXP2, the greater reduction of forecast error on the background trajectory results in a smaller FER, as the forecast from the background and the forecast from the analysis are drawn closer together. Therefore, these results demonstrate that an improvement of the analysis–forecast system can be coincident with a smaller FER.

### b. Observation impact

Figure 4a shows the observation impact of 16 different observation types for the three experiments in descending order with respect to EXP1 (see Table 1 for descriptions of these observation types). For EXP1, SOUND has the largest observation impact followed by AMSUA, SYNOP, QSCAT, conventional AMV, METAR, PILOT, SHIPS, GPSPW, BUOY, AIREP, and PROFILER. This result is similar to that of Jung et al. (2013), who calculated observation impact based on a 6-h forecast. The rank of observation types by impact for EXP0 is similar to that of EXP1, and the time series of impact by type is similar as well (not shown). In EXP2, the observation impact of the enhanced AMVs is large compared to the impact of conventional AMVs, smaller than SOUND and AMSUA but larger than SYNOP, and other types of observations are ranked similarly to EXP1. Relative to EXP1, observation impacts for most observation types decrease when the 1-h AMVs are assimilated in EXP2.

Figure 4b shows the 24-h observation impacts of six different observation variables in the three experiments ranked in descending order with respect to EXP1. For all experiments, brightness temperature (TB) shows the largest observation impact, followed by horizontal wind vector components (*U* and *V*). While TB still expresses the largest observation impact among all variable types in EXP2, the impact is smaller compared to EXP0 and EXP1, and the observation impact from *U* and *V* observations increases. In EXP2, nonwind variables of TB, temperature *T*, specific humidity *Q*, and pressure *P* express a decreased observation impact compared with their impact in EXP0 and EXP1, showing the effect of the 1-h AMVs on the assimilation and the impact of other observation types.

The influence of enhanced AMVs on other observation/variable types can be explained through background error covariance established for optimal linear analysis [Eq. (5)]. The error covariances represent the relationship between perturbations in one part of the model state with perturbations elsewhere, horizontally, vertically, and across variables. When the impact of enhanced AMV *U* and *V* observations reduces the impact of another variable type (such as TB), one can assume that either 1) prior to the assimilation of enhanced AMVs, the TB observations were constraining the winds through background error covariance, and no longer need to do so once the enhanced AMVs are assimilated, reducing the impact of TB observations, or 2) after the assimilation of enhanced AMVs, the wind observations are constraining TB through background error covariance more than they used to, reducing the impact of TB observations.

The forecast error [Eq. (10)] can be separated into component parts, with a kinetic energy component for *U* and *V*, and an available potential energy component for *T*. On average, the 24-h forecast error (error on the analysis trajectory) for *U* and *V* in EXP2 is reduced by 4.4% relative to EXP0 and 1.3% relative to EXP1, and the 30-h forecast error (error on the background trajectory) for *U* and *V* in EXP2 is reduced by 5.2% relative to EXP0 and 2.0% relative to EXP1. In contrast, the 24-h forecast error (error on the analysis trajectory) for *T* in EXP2 is reduced by 1.8% relative to EXP0 and 1.4% relative to EXP1, and the 30-h forecast error (error on the background trajectory) for *T* in EXP2 is reduced by 1.9% relative to EXP0 and 1.4% relative to EXP1. Therefore, by assimilating enhanced AMVs, the wind forecast errors are reduced primarily, but the forecast errors associated with the temperature are also reduced through the background error covariance. These forecast error reductions explain the higher observation impact of the enhanced AMVs and wind variables.

Figure 5 shows the observation impact of radiances sorted by satellite, channel, and experiment. In EXP2, the observation impact of AMSUA decreases on average, especially for channel 7, which is mainly weighted in the upper troposphere, where the increase in AMVs is observed when enhanced AMVs are assimilated (Fig. 6). Therefore, as might be expected, the reduced impact from the TB observations largely comes from locations where TB observations and enhanced AMVs overlap.

### c. Normalized observation impact

Figure 7a shows the impact divided by the number of observations for 16 different observations types for the three experiments, with observation types ranked in descending order with respect to EXP1. For EXP1, GPSPW has the largest normalized observation impact followed by SYNOP, PROFILER, SOUND, PILOT, BUOY, METAR, METOP-2, NOAA-18, AIREP, NOAA-16, NOAA-15, SHIPS, conventional AMV, and QSCAT. The ranks of four kinds of AMSUA observations are relatively smaller when compared with that of the total observation impact in Fig. 4a. The normalized observation impact of the 1-h AMVs ranks toward the middle of the order in EXP2.

Figure 7b shows 24-h normalized observation impacts for observation variables, ranked in descending order with respect to EXP1. TB is the variable that expresses the largest total impact (Fig. 4b), whereas *P* is the variable that shows the largest per-observation (normalized) impact (Fig. 7b) for most of the experiments. For EXP1, the rank of the other observations is followed by *U*, TB, *T*, *V*, and *Q*, which is similar to the order for EXP0. The normalized observation impacts of pressure *P*, horizontal wind vector (*U* and *V*), and other variables (TB, *T*, and *Q*) show a decreasing trend when enhanced AMVs are assimilated in EXP2. This could reflect the large number of observations that are contributing similar information to the forecast.

### d. Fraction of beneficial observations

Figure 8a shows each observation type’s fraction of beneficial observations in descending order, ranked with respect to EXP1. In EXP1, GPSPW has the largest value followed by NOAA-18, QSCAT, NOAA-16, BUOY, SYNOP, METAR, METOP-2, NOAA-15, SOUND, AIREP, SHIPS, PROFILER, PILOT, and conventional AMV. Those observation types with a small number of observations, such as GPSPW, have a high fraction of beneficial observations, whereas observation types with large numbers of observations, such as AMVs, show a relatively smaller ratio in EXP1. However, in EXP2, the fraction of beneficial observations for both conventional and enhanced AMVs shows a relatively larger ratio, which is consistent with the higher ranks in total impact (Fig. 4a).

Figure 8b presents the fraction of beneficial observations sorted by observation variables in descending order, ranked with respect to EXP1. In this result, *P* has the largest value, followed by TB, *V*, *U*, *T*, and *Q*. For most observation types and variables, the fractions of beneficial observations in the three experiments are similar. According to Gelaro et al. (2010), the fraction of beneficial observations in global models is slightly larger than 50%. However, in all experiments in this study, which uses a regional model, the fraction is over 60% for most observation types and variables, similar to that in Jung et al. (2013).

### e. TC track forecasts

Figure 9 presents the JMA RSMC best tracks of two TCs, Sinlaku and Jangmi, which occurred during September 2008. The two typhoons both formed between 10°–20°N and 120°–140°E. Sinlaku started to develop from 1800 UTC 8 September 2008 and moved north-northwest during its early development. It changed course near Taiwan (Formosa) to a northeast direction, then passed by the southern coast of the Japanese Isles (Kyushu, Shikoku, Honshu) before dissipating at 1800 UTC 20 September. Jangmi formed at 1200 UTC 24 September and followed a track similar to that of Sinlaku, but dissipated before it reached Kyushu at 1800 UTC on 30 September. Figure 9 also shows the TC tracks of the three experiments from their respective analysis states.

Figure 10 shows center position errors of the two TCs for the analysis and 24-h forecast in latitude, longitude, and distance. For each TC and experiment, the distance error of the analysis is always smaller than that of the 24-h forecast. In the case of Sinlaku, the errors in latitude, longitude, and distance, for both the analysis and 24-h forecast, generally decrease when conventional AMVs are assimilated. However, the mean differences in the analysis and 24-h forecast center position distance errors between EXP1 and EXP0 are not statistically significant based on a Student’s *t* test at 90% confidence. In EXP2, both the analysis and 24-h forecast distance error decrease more significantly when the enhanced AMVs are assimilated. The mean difference in the analysis distance error between EXP2 and EXP0 (EXP2 and EXP1) is statistically significant at 99% (90%) confidence. The mean difference in the 24-h forecast distance error between EXP2 and EXP0 is statistically significant at 90% confidence, whereas that between EXP2 and EXP1 is not statistically significant at 90% confidence. For Jangmi, including the enhanced AMVs decreases the analysis error and 24-h forecast error compared with EXP0 and EXP1. Generally, the mean differences in the analysis and 24-h center position distance errors between EXP2 and EXP0 or EXP1 are statistically significant at ~90% confidence.

During the period of the TCs, the 24-h forecast error for *U* and *V* in EXP2 is reduced by 4.9% relative to EXP0 and 1.2% relative to EXP1, whereas the 24-h forecast error for *T* in EXP2 is reduced by 1.6% relative to EXP0 and 1.0% relative to EXP1, which is a higher (lower) forecast error reduction for winds (temperature) compared to that during the whole experimental period. Small position errors in the forecast position of a TC center can contribute significantly to wind errors overall, since a small position error of the TC vortex can impose large errors in wind speed and direction near the TC. It is therefore expected that the modest track improvement witnessed for TCs occurring during this experiment contribute to a larger reduction in total wind error than total temperature error.

Figures 11a and 11b show the average 5870-gpm height contour at 500 hPa from 0000 UTC 12 September to 0000 UTC 13 September (i.e., during Sinlaku) with each cycle’s experimental track and the best track. Likewise, Figs. 11c and 11d show the same result for Jangmi from 0000 UTC 26 September to 0000 UTC 27 September. According to Tu et al. (2009), the 5880-gpm geopotential height contour at 500 hPa is generally appropriate for describing the realm of the subtropical high in the western North Pacific–East Asia (WNP-EA) region. Therefore, TC tracks tend to parallel the 5880-gpm contour. Instead of 5880 gpm, the 5870-gpm contour is illustrated in this study because the 5870-gpm contour shows more clear features. In Fig. 11a, the 5870-gpm contour of EXP2 is positioned slightly more eastward (in the north-east direction) than that of the other two experiments, so the center is closer to the best track value. In Fig. 11d, the contour of 5870 gpm is located slightly more northward (in the northwest direction) in EXP2 than EXP0 and EXP1; thus, the center is closer to the best-track value. This suggests that the enhanced AMVs are not only improving the steering wind fields but also the mass (height) fields.

## 5. Summary and discussion

The performance of NWP is advancing rapidly thanks to an increasing number of available satellite observations, such as enhanced AMVs or AMSUA radiances, as well as improvements to data assimilation techniques that prepare the initial analyses for the numerical model forecasts. Since data assimilation is used in short-, medium-, and long-range (climate range) NWP, how various observations impact the forecasts is the subject of quantitative evaluation methods. One of the traditional methods used to perform this evaluation is OSEs, which normally demand a significant amount of resource time for the assessment of each observation’s effect. The adjoint method is an alternative way and uses less time for computation, while providing reasonable estimates of impact for each observation individually.

In our WRF forecast experiments, a control without any AMV observations assimilated (EXP0) and a second experiment with just operational AMVs assimilated (EXP1) found that the largest observation impact on 24-h forecasts comes from radiosondes. Operational AMVs contribute to a modest reduction in forecast error in EXP1. Upon assimilation of enhanced AMVs (EXP2), the reduction in forecast error along both the analysis and background trajectories and the observation impact of enhanced AMVs becomes much larger, ranking them right below radiosonde and AMSUA radiances. GPSPW has the largest normalized observation impact among all observation types.

The forecast is improved by the assimilation of operational and enhanced AMVs, with smaller forecast errors along both the analysis trajectory and the background trajectory. Error reduction is larger on the background trajectory, so the total observation impact across all observations (the linear FER) becomes smaller, which is consistent with a smaller nonlinear FER computed directly from the forecast and verifying analysis fields. These results demonstrate how an improvement to the analysis–forecast system, even through the assimilation of novel observations, can ultimately yield a smaller FER.

In EXP2, AMSUA’s channel 7, which mainly contributes to temperature observations in the upper troposphere, has the reduced observation impact. This implies that the effect of enhanced upper-level AMV data overlaps with that of the AMSUA’s channel 7. The fraction of observations that is beneficial to the forecasts is found to be approximately 60% for all three experiments, but with a small increase in the ratio in EXP2 when enhanced AMVs are assimilated. This value is larger than what is typically cited with global models (50%–55%).

Finally, the impacts of the enhanced AMVs on TC track forecasts were examined. Forecast errors of western North Pacific Typhoons Sinlaku and Jangmi from 2008 decrease when enhanced AMVs are assimilated. The 24- and 30-h forecast errors associated with model wind variables are reduced primarily, but those variables associated with temperature (geopotential height) are also improved through the background error covariance. These results show the influence of the enhanced AMVs spreads to other observation/variable types.

An investigation into the effect of lateral boundary conditions on the adjoint-based observation impact estimation in a regional model is currently under way as a follow-on to this study.

## Acknowledgments

This research was supported by the Korea Meteorological Administration Research and Development Program under Grant KMIPA 2015-5200. The authors appreciate three reviewers for their valuable comments and Dave Stettner of CIMSS for providing the enhanced AMV datasets used in this study.

## REFERENCES

*Atmospheric Modeling, Data Assimilation and Predictability*. Cambridge University Press, 341 pp.

*2010 Fall Meeting*, San Francisco, CA, Amer. Geophys. Union, Abstract A41B-0070.

*Data Assimilation: Making Sense of Observations*, W. Lahoz, B. Khattatov, and R. Menard, Eds., Springer, 647–679.

## Footnotes

© 2017 American Meteorological Society.

This article is licensed under a Creative Commons Attribution 4.0 license (http://creativecommons.org/licenses/by/4.0/).