1. Introduction
Observing system experiments (OSEs) are commonly used for evaluating the impact of observations on data assimilation systems. OSEs enable us to quantify the impact of observations in specific regions or of type, by excluding them from or adding them to the total observations assimilated into a data assimilation system. OSEs are usually used to evaluate the direct influence of observations on weather phenomena occurring over regions at all distances, from the local to the global domains (e.g., Weissmann et al. 2011; Ito et al. 2018; Sato et al. 2017; Schäfler et al. 2018); they are also used to estimate the total impact of some observation types or observations in specific latitudinal bands on the global observing system (e.g., Bormann et al. 2019; Day et al. 2019; Lawrence et al. 2019). In previous work, we have conducted many OSEs using in-house developed data assimilation system known as the Atmospheric General Circulation Model for the Earth Simulator—a local ensemble transform Kalman filter (AFES-LETKF) ensemble data assimilation system (ALEDAS; see appendix A). This system has been used to generate an experimental atmospheric global ensemble reanalysis (ALERA2). So far, these studies have focused on the remote influences of small subsets of observations obtained during field campaigns (e.g., Inoue et al. 2013; Yamazaki et al. 2015). To clarify how observation impacts propagate and where their impacts accumulate in quasi-operational data assimilation and forecast systems can provide useful information for the design of observational campaigns. However, conducting OSEs during a campaign is not very practical because they are too expensive in computational resources and time, as additional data assimilation and forecast cycles must be performed to evaluate specific observations.
Alternatively, the forecast sensitivity to observation (FSO) technique pioneered by Langland and Baker (2004) allows us to diagnose the impacts of all observations by quantifying the extent to which each observation improves or degrades subsequent forecasts. FSO estimates (diagnoses) individual observation impacts at early short-range forecast times, which are typically 6–24 h. In this study we adopt the acronym FSO instead of FSOI (forecast sensitivity observation impact) also used in many previous studies (e.g., Sommer and Weissmann 2016). The FSO formulation has been originally developed for variational data assimilation systems as the adjoint-based FSO. Recent studies by Liu and Kalnay (2008) and Kalnay et al. (2012) have applied the formulation to the ensemble Kalman filter (EnKF) system, known as the ensemble-based FSO (called EFSO). The EFSO diagnosis can be used in current data assimilation schemes. Recently, Kotsuki et al. (2019) showed the usefulness of EFSO in a nonhydrostatic model. Alongside the global NWP model, Sommer and Weissmann (2016) and Necker et al. (2018) successfully adopted the EFSO diagnosis for a convection-permitting regional model. The adjoint-based FSO and EFSO diagnoses can be used to quantify the impact of each observation individually, without the need to conduct OSEs. The adjoint-based FSO and EFSO techniques have been successfully used to estimate the impacts of specific observation types (e.g., satellite observations) against conventional ones (e.g., Gelaro and Zhu 2009). Recently, Lien et al. (2018) proposed the use of the EFSO diagnosis in an offline approach to develop new data selection strategies. Elsewhere, Ota et al. (2013) and Hotta et al. (2017) proved that the EFSO technique can be used for the proactive quality control of observations.
Previous studies used the adjoint-based FSO and EFSO techniques for targeted observations. In targeted observations (Majumdar 2016), one deploys and assimilates additional observations through an observational campaign to improve the numerical forecast of a weather event. Since targeted observations are conducted to better forecast weather events that occur near campaign sites, an FSO diagnosis that estimates a forecast impact in less than a day would be most useful. However, it is not known yet whether the adjoint-based FSO or EFSO is useful for estimating the remote impacts of observations or impacts on time scales longer than a day. This may be desirable for field campaigns conducted from ships or near-stationary mobile platforms.
In the adjoint-based FSO and EFSO context the observation impact represents the difference between a selected measure of error on the analysis and background model state trajectories (see section 2a and Fig. 1). In this study, we define observation impacts obtained by actual data assimilation cycles (OSEs) as OIOSE and those estimated by the EFSO technique which has been implemented as OIEFSO.
Our purpose is to understand how well EFSO can estimate OIOSE of individual observations and their downstream influence. We also aim to understand which points are most influential on short- and/or medium-range weekly forecasts; in other words, we seek to discover the “optimal spot” of observational locations to enhance global NWP forecasts. To the best of our knowledge, only a few recent studies directly compared the adjoint-based FSO and EFSO diagnoses and OIOSE obtained by data-denial experiments in the global observing framework. Gelaro and Zhu (2009) compared the values obtained from the adjoint-based FSO with those obtained from data-denial experiments. For satellite observations they used the adjoint-based FSO technique to estimate the relative contributions by observation type, with a focus on conventional and satellite observations. Ota et al. (2013) conducted a data-denial experiment for a case where several satellite-wind observations that were estimated as candidates to degrade a forecast by EFSO. They showed that the estimation could capture the actual 24-h forecast change. Hotta et al. (2017) further developed the study of Ota et al. (2013) and proposed the concept of “proactive QC (quality control)” in which observations with the potential to degrade a forecast could be detected by EFSO and rejected during the data assimilation process. Very recently, Lawrence et al. (2019) compared observation impacts estimated by the adjoint-based FSO with OIOSE from data-denial experiments to study how Arctic observations influence global weather forecasts. They found that the relative contributions of observation types obtained by the adjoint-based FSO technique were consistent with the results of the data-denial experiments for short and even medium forecast ranges. The aforementioned studies illustrated that adjoint-based FSO and EFSO techniques are useful for estimating OIOSE on short- and medium-range forecasts. Their focus, however, was on large numbers of globally distributed observations rather than on small subsets obtained through observational campaigns.
To demonstrate the usefulness of EFSO for evaluating OIOSE on short- and medium-range forecasts and for estimating the remote impacts of localized observations obtained in field campaigns, we need to address the following question:
Can the EFSO technique reasonably approximate the short-range OIOSE obtained by data-denial experiments?
Are initial (at an early short-range forecast) OIOSE estimated by the EFSO diagnosis are dynamically propagated in the forecast to retain their impacts on longer forecasts?
Which is the most important for improving medium-range weather forecasts the Arctic, the midlatitudes, or the tropics?
2. Implementation of EFSO in ALEDAS
ALEDAS is a global atmospheric data assimilation system that combines AFES (an AGCM) with the LETKF (an EnKF). See appendix A for detailed configurations.
a. Physical interpretation of the observation impact and its approximation by EFSO
In this subsection, we define the observation impact, give a physical interpretation, and discuss how it can be approximated by the EFSO technique.The details of the EFSO formulation are available in Kalnay et al. (2012), Ota et al. (2013), and Hotta et al. (2017).
1) The total observation impact (total OIOSE)
The total OIOSE at the evaluation lead time te obtained by the difference between
2) The EFSO approximation
Because
3) The matrix and the difference between the forecast errors
b. Implementation
To calculate OIEFSO, we need to select several parameters. The target domain of EFSO is set to the global domain. The evaluation lead time te is mainly set to 6 h. The moving localization scheme (Ota et al. 2013; Hotta et al. 2017) with coefficient 1.0 is adopted, in which the localization function is advected by the wind fields of
In this paper, we use as our reference
The reasons for evaluating at lead time 6 h rather than at longer ones are as follows.
The 6-h EFSO has a much lower computational cost. An additional process that one substantially uses to calculate is extended forecasts for 3 h (See appendix A).
The 6-h EFSO suffers less from the impact of the moving localization scheme than EFSO with longer evaluation (lead) times (Hotta et al. 2017; Kotsuki et al. 2019). It would be difficult to determine the optimal weighting coefficient of the moving localization, since OIEFSO can be propagated in the Lagrangian way and by the Rossby wave transport owing to phase and group velocity (Kalnay et al. 2012). For example, Ota et al. (2013) chose the coefficient 0.75 for 24-h EFSO in an operational global data-assimilation system.
c. Evaluation
We first examine whether the implemented EFSO technique works correctly in ALEDAS. ALEDAS forecast–analysis cycles with EFSO diagnoses are examined for the period of December–February 2015/16 (Fig. 2).
Total OIEFSO
The distribution map of the winter-averaged OIEFSO values
3. Experimental designs
To use the EFSO diagnosis as an alternative to an OSE, the extent to which a 6-h EFSO can estimate the individual OIOSE for short- and medium-range forecasts must be examined. In this study, we conduct multiple data-denial experiments for various regions in the Northern Hemisphere and in the tropics, where radiosondes are routinely launched.
The experiments are conducted from 1 December 2015 to 29 February 2016. During this period, 7-day ensemble forecasts are initialized every day from 0000 UTC using ALERA2 (Fig. 4); that is, 91 times of 7-day forecast experiments (Fig. 4). This is our control experiment (CTL hereafter).
We compare CTL with 12 data-denial experiments (OSEs). In each of these experiments, a subset of radiosonde observations from three adjacent sites is excluded. Four locations are in the midlatitudes (20°–60°N), four in the Arctic (60°–90°N), and four in the tropics (10°S–10°N), as shown in Fig. 5. The midlatitude locations are hereafter denoted as the Mid, Mid2, Mid3, and Mid4 experiments (black symbols in Fig. 5); the Arctic locations as Pol, Pol2, Pol3, and Pol4 experiments (blue symbols); and the tropical locations as Tro, Tro2, Tro3, and Tro4 experiments (red symbols). After the data denial, 7-day ensemble forecasts are initialized every day from 0000 UTC using OSE analyses (Fig. 4); that is, 91 times of 7-day forecast experiments for each OSE. Note that the data denial in the data assimilation process is not repeated to avoid the temporal accumulation of OIOSE; i.e., the data denial is only performed once before each forecast. These non-repeated data-denial experiments will help us to understand how OIOSE propagate dynamically. Each CTL and OSE ensemble forecast is initialized from the 63 members of the CTL (ALERA2) and OSE analyses. To evaluate the OIOSE in each OSE, we compare the ensemble forecast mean of CTL
The OIEFSO of a specific OSE
We first compare
4. Results
a. Comparison of OIOSE and OIEFSO
We compare the 6-h OIEFSO
To elucidate to what extent EFSO has potential to estimate OIOSE within short-range forecasts, we compare
In the next step, we examine whether the 6-h EFSO-derived
Figure 8 shows the time sequences of
The figure reveals that among each latitudinal band (each color in Fig. 8) the relative differences (rankings) of the 6-h (initial) OIOSE remain unchanged up to lead times of 1 to 2 days except for Mid2. Only the relative ranking of
Starting from lead times of 3 days, however, the relative rankings do not remain intact as the time series of
It is worth mentioning that
b. Propagation of OIOSE
The results so far indicate that, for short-range forecasts, EFSO is useful to estimate the globally averaged OIOSE, but not for medium-range forecasts. However, when we focus on the distributions of OIOSE in medium ranges, that is,
First, we examine the temporal evolution of OIOSE [
During the short-range and the early medium-range forecasts (Days 1–3), beneficial OIOSE mainly propagates dynamically; in other words, they are propagated in the Lagrangian way (by wind advection) and by the Rossby wave transport owing to phase and group velocity (Moteki et al. 2011; Inoue et al. 2013; Yamazaki et al. 2015; Hattori et al. 2017; Sato et al. 2020b). We, hereafter, refer to this mechanism as dynamical propagation. In the Pol experiment, initial OIOSE in northern East Siberia propagates southward and eastward and extends over the Arctic Ocean. In the Mid4 experiment, initial OIOSE propagates eastward (downstream) with the westerly jet. In the Tro experiment, initial OIOSE over the western central Pacific shifts westward with the prevailing trade winds. All these patterns are consistent with dynamical propagation.
Again to justify OIEFSO, we compare the distributions of
In the medium range (Figs. 11a–c), however, many spots of nonbeneficial OIOSE appear and both beneficial and nonbeneficial OIOSE grow in the midlatitudes after Day 4, regardless of the latitudinal band of the data denial. This explains the sign changes of the globally averaged
During the medium range, the regions of amplified OIOSE irrespective of beneficial or nonbeneficial ones seem to be concentrated in the midlatitudes, because standard deviations of
The beneficial and nonbeneficial OIOSE in the Pol experiment in medium range broadly extend throughout the Arctic and toward the midlatitudes (Figs. 11a,d), and beneficial OIOSE are distributed in the midlatitudes more broadly than those in the Mid4 and Tro experiments (Figs. 11a–c). Therefore, Arctic observations can be the most influential and can have broadest beneficial OIOSE regions even for medium-range forecasts. If the amplified initial OIOSE by the Arctic observations systematically propagates via dynamical propagation toward the midlatitudes, beneficial OIOSE areas can appear downstream of the propagation in the midlatitudes.
Dynamical propagation of the OIOSE of the Arctic observations for medium range forecasts is examined by composite maps of OIOSE during Days 0.25–3 and Days 4–7 (medium ranges) for the 4 Arctic OSEs (Figs. 12a,b). During the short range, beneficial Arctic OIOSE originating from the initial observation points amplifies within the Arctic regions (Fig. 12a). In the medium range, areas of beneficial OIOSE are found at the east coast of North America and over the northeastern Pacific in the midlatitudes (Fig. 12a). The former area is possibly due to dynamical propagation of the initial Arcitic OIOSE. The dynamical propagation is partly illustrated by vertically averaged flux of OIOSE for the Arctic OSEs as composite of
To further examine the dynamical propagation, we plot the time evolution of the
Note that there can be two possible major propagation routes for the Arctic OIOSE over North America. One is along the surface. This propagation can be caused by meridional direct circulations in the extratropics; this is suggested by the pattern of
In addition, the composite map in the medium range for the Arctic OSEs evidently shows different features than those in the midlatitude and tropical OSEs (Figs. 12b–d); areas of beneficial OIOSE are found within the Arctic Circle and at the east coast of middle North America. For the midlatitude and tropical OSEs, an area of the beneficial OIOSE is found over the northeastern Pacific; however, such beneficial area is also found for the Arctic composite map. Therefore, the beneficial OIOSE area over the northeastern Pacific is not related to dynamical propagation.
In summary, the following points are found.
OIOSE are able to dynamically propagate during short-range forecasts, irrespective of latitude.
For the medium-range forecasts, the Arctic OIOSE most effectively amplify and dynamically propagate.
Areas of systematic beneficial OIOSE during medium-range forecasts over the Arctic circle and the east coast of middle North America are associated with Arctic observations.
c. Discussion: Comparison with repeated OSEs for the Arctic experiments
Finally we discuss how the results above can provide useful information when observations over a limited geographical region are repeatedly collected, which is common in field campaigns. In this case, OIOSE accumulate in the analysis field (e.g., Yamazaki et al. 2015; Sato et al. 2020b). Here we test the Arctic observations because the Arctic OIOSE can most effectively amplify and propagate OIOSE in the short- and medium-range forecasts.
In section 3, the data denial was not repeated for any OSE (non-repeated OSEs hereafter). Here, we conduct two additional data assimilation and forecast experiments for each Arctic OSE, namely the repeated OSE (rep-OSE) and the semi CTL (semi-CTL) forecast experiments. Here, the rep-OSEs are conducted for the Pol, Pol2, Pol3, and Pol4 observations. For example, the rep-Pol analysis is the same analysis of ALERA2 (red arrow in Fig. 4) except the Pol observations for every 0000 UTC (rep-Pol analysis). In the rep-OSE analysis, data denials are repeated during the winter. The semi-CTL analysis is generated from the rep-OSE analysis but with one data-assimilation process for adding the OSE (e.g., Pol) observations every day at 0000 UTC (semi-CTL analysis). This is similar to generating a non-repeated OSE analysis, as described in section 3 (blue circles in Fig. 4). As in the non-repeated OSE, 7-day forecast experiments are conducted initialized with the rep-OSE and the semi-CTL analyses at every 0000 UTC during winter (91 times for each forecast experiment). The OIrep-OSE [
Time sequences of
Amplification and dynamical propagation of
Interestingly, the beneficial regions of OIrep-OSE and OIOSE are consistent with Jung et al. (2014), in which the influence of Arctic atmospheric reproducibility (observation impact) improved the medium-range forecast in the midlatitudes, especially in North America (their Fig. 2).
Therefore, non-repeated OSEs and their OIEFSO can provide useful information on the outcome of repeated OSEs, such as obtained during long-term observational campaigns. It would be interesting topic for future studies to compare repeated and non-repeated OSEs in other latitudinal bands.
5. Conclusions
We have successfully implemented the EFSO technique in the AFES-LETKF data assimilation system (ALEDAS). Based on this system, we have investigated whether the 6-h EFSO diagnosis can approximate the results of OSEs.
We conducted 12 OSEs in each of which a subset of radiosondes launched at three neighboring sites was excluded from the data assimilation. To obtain the observation impacts (OIOSE), we compared these experiments with the control experiment, in which all radiosondes were included. The 12 observation sites were selected from the Northern Hemisphere (4 in the Arctic, 4 in the midlatitudes, and 4 in the tropics). Through non-repeated data-denial experiments for the winter (December–February) of 2015/16, we have examined to what extent the 6-h OIOSE obtained by the OSEs are estimated by the EFSO technique. Our results suggest that the winter-averaged EFSO technique can accurately estimate 6-h OIOSE in all three latitude bands (Arctic, midlatitudes, tropics).
We have also tested whether the observation impacts estimated by EFSO (OIEFSO) obtain at lead time 6 h can provide information on OIOSE at short- (1–2 day) and medium-range (3–7 day) forecasts. For short-range forecasts, EFSO well estimated OIOSE at all latitudes. Furthermore, by focusing on spatial distribution of OIOSE, Arctic OIOSE in the short range tended to amplify within the Arctic. During the medium range, these OIOSE dynamically propagated and remained beneficial over several regions: the Arctic Circle and the eastern coastal region of middle North America. Therefore, we conclude that the EFSO technique can be useful to estimate OIOSE in short-range forecasts at all latitudes, and in medium-range forecasts for the Arctic. We have also performed four repeated Arctic OSEs that mimicked Arctic field campaigns covering the winter period. The results showed consistent evolution and dynamical propagation of Arctic observation impacts obtained from the repeated OSEs that are similar to OIOSE from the non-repeated OSEs. This implies that the results from the non-repeated Arctic OSEs and estimations by EFSO can provide valuable information for repeated Arctic observation campaigns of YOPP.
In other words, our results show that, for medium-range forecasts, the Arctic observations can be the most influential. They can have therefore the highest potential for improving medium-range forecasts in the Northern Hemisphere. Based on the discussion in sections 4b and 4c, we summarize the factors why the Arctic observations can be the most influential.
The small number of Arctic observations. The Arctic regions are still relatively poorly observed (e.g., Jung et al. 2016, and Fig. 16a). Thus, Arctic observations tend to have a relatively large OIEFSO (Fig. 16c). We note, however, that the tropospheric observation density (observations per km2), is not very different between the Arctic and tropics (Fig. 16b).
Due to the existence of the extratropical direct meridional circulation toward the midlatitudes and due to the ubiquitous Rossby waves in the extratropical upper troposphere, the Arctic OIOSE propagate toward the midlatitudes.
Choice of error norm (metric) for quantifying OIEFSO and OIOSE. We chose the globally averaged moist total energy, which may emphasize errors on midlatitude storm-track regions (Figs. 11d–f). This choice is motivated by our interest in the midlatitude storm tracks, which are one of the most important elements of the general circulation.
Acknowledgments
The authors thank the organizer and the participants of the workshop “Observational Campaigns for Better Weather Forecasts” held at ECMWF in June 2019 (Magnusson and Sandu 2019), which inspired and helped us summarize the paper. We are grateful to Dr. Ingo Richter for his thoughtful comments to improve the paper and English language assistance. We also would like to thank three anonymous reviewers, and Drs. Daisuke Hotta and Yoichiro Ota for their helpful comments. The ALERA2 dataset is available from http://www.jamstec.go.jp/alera/alera2.html. This work was supported by JSPS KAKENHI (26282111, 15H02129, 17K05663, 18K13617, 18H03745, 18KK0292, and 19H05702), and the Arctic Challenge for Sustainability Research Project (ArCS) by MEXT. Numerical simulations were conducted on the Earth Simulator with the support of JAMSTEC.
APPENDIX A
ALEDAS
The ALEDAS configuration used in the present study is described in Yamazaki et al. (2015): The horizontal resolution is T119, which roughly corresponds to a 1° × 1° latitudinal and longitudinal horizontal resolution. There are 48 vertical levels, with the top at 3 hPa. The ensemble size is 63. The uniform multiplicative 10% inflation method is used. The horizontal and vertical localization scales of the LETKF are set to 400 km and 0.4lnp, respectively (Miyoshi et al. 2007; Enomoto et al. 2013; Yamazaki et al. 2017). Observations include conventional types and satellite winds, which are prepared from the PREPBUFR datasets, compiled by the National Centers for Environmental Prediction (NCEP) and archived at University Corporation for Atmospheric Research (UCAR). ALERA2 can reasonably well reproduce the observed synoptic–large-scale atmospheric circulations (Fig. A1). Further details of ALEDAS and ALERA2 can be found in Miyoshi and Yamane (2007), Enomoto et al. (2013), and Yamazaki et al. (2017).
ALEDAS has been used to evaluate impacts of observations obtained in observational campaigns in various regions for various seasons; the Arctic Ocean (Inoue et al. 2013; Yamazaki et al. 2015; Sato et al. 2017, 2018b, 2020b), midlatitudes (Kawai et al. 2017; Sato et al. 2020b), the Philippine Sea (Hattori et al. 2017), the Southern Ocean (Sato et al. 2018a), and the Antarctic (Sato et al. 2020a) during summer (Yamazaki et al. 2015; Kawai et al. 2017; Sato et al. 2018a,b, 2020a), fall (Inoue et al. 2013; Hattori et al. 2017; Sato et al. 2020b), and winter (Sato et al. 2017).
Flowchart of forecast–analysis cycles in ALEDAS are shown in Fig. A2. In terms of code modifications to calculate the 6-h EFSO diagnosis, we must additionally calculate
APPENDIX B
Seasonal OIEFSO Values and the Values during the Special Observing Periods
ALEDAS and the EFSO diagnosis continued until winter 2019. We show the seasonality of OIEFSO for the whole globe. Figure B1 shows the seasonal averages of the OIEFSO values of the radiosondes. We can find two features common to all seasons; (i) the OIEFSO values are smoothly distributed, and (ii) the OIEFSO values are larger in the higher latitudes.
The same features are found in the maps during special observing periods (SOPs) of the Year of Polar Prediction (YOPP, Jung et al. 2016; Bromwich et al. 2020) when the extra radiosonde observations were performed (i.e., the polar observations were extremely increased) at many routine stations and mobile stations by field campaigns in the Arctic or Antarctic regions (Fig. B2).
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