Assumptions about prior fossil fuel inventories impact our ability to estimate posterior net CO₂ fluxes that are needed for verifying national inventories

Success of the Paris Agreement (UNFCCC 2023a) relies on accurately monitoring and verifying collective global greenhouse gas (GHG) emissions reduction efforts. We cannot afford not to have these systemic checks and balances if we are to minimize further global mean surface warming of Earth. Following preceding environmental protocols, such as the Kyoto protocol (UNFCCC 2023b), national emission inventories (NEIs) will play a key in role in planning and reporting reductions in GHG emissions. The emission reporting is a minimal regulatory obligation under the Paris Agreement by all submitting parties, including countries who had not reported a NEI under the previous Kyoto Protocol, unlike developed nations called Annex I countries. Robustness of inventory estimates requires a clear, transparent, and consistent framework for data collection, analysis, and compilation. In addition to the inventory capacity building for the new inventory submissions, the enhanced evaluation and verification of reported inventory estimates (e.g. IPCC 2019) should further reinforce the global emission reduction monitoring and assure the global compliance of pledged climate mitigation efforts (e.g. nationally determined contribution (NDC)); however, due to the nature of the activity-data based emission calculation (e.g. IPCC 2006), where emissions are assumed to be proportional to activity levels, even with an established framework, inventory emission estimates are intrinsically prone to systematic biases due to emission factors and activity data used (e.g. Guan et al 2012, Liu et al 2015). Assuring the accuracy of NEI emission estimates is critical in the technical assessment of our climate mitigation progress towards the temperature goal (Weir et al 2022).

The use of atmospheric data for evaluating and verifying GHG emissions has been extensively examined over the past decades (e.g. NRC 2010, NAMES 2022). Generally, changes in the atmospheric concentration of trace gases are due to emissions, uptake, and atmospheric chemistry and transport. In the case of atmospheric CO₂, changes are largely determined by fluxes (emissions minus uptake) and atmospheric transport (e.g. Palmer et al 2008). Atmospheric CO₂ flux inversions take advantage of the information provided by atmospheric data to CO₂ flux estimates (e.g. Tans et al 1990, Gurney et al 2002). While flux inversions started as an approach to estimate the size and location of large-scale sources and sinks (e.g. Tans et al 1990, Gurney et al 2002), the methods are now widely recognized as a potential tool for the QA/QC and verification of NEIs (e.g. IPCC 2019). Atmospheric top-down approaches also provide an opportunity for determining national emission estimates from countries that do not currently have the infrastructure to robustly provide bottom-up emission estimates. NEIs provide annual country level emissions, while the Paris Agreement recognizes the subnational key actors as the driving force for the progress. Atmospheric top-down approaches should be also able to fill the information gaps and provide actionable estimates for key sub-national targets, such as states, provinces, cities, subject to data coverage.

Top-down flux estimation methods rely on prior emission estimates and meteorological reanlayses to drive the atmospheric transport model to determine 3D atmospheric concentrations of CO₂ that are subsequently sampled subject to the instrument sampling configurations. Most inverse methods use Bayes' theorem to fit optimal distributions of CO₂ fluxes that minimize the mismatch between model and observations of CO₂, subject to model and measurements uncertainties. The resulting posteriornet fluxes of CO₂ are consistent with prior knowledge and measurements, and their uncertainties. A common approach adopted by top-down flux estimation methods is then to subtract the prior fossil fuel emissions from the posterior net flux estimates to quantify natural fluxes (e.g. Gurney et al 2005, Wang et al 2020, Byrne et al 2023). First, this implicitly assumes perfect knowledge of fossil fuel CO₂ emissions (FFCO2, roughly corresponding to emissions from energy sector). Consequently, the prior model and observation mismatch (and the associated uncertainties) is attributed exclusively to incorrect natural biosphere fluxes. FFCO2 is not corrected in this process so errors in the magnitude of FFCO2 will be redistributed to the posterior flux estimate for the natural biosphere. This limits the current use of top-down estimates for evaluating country emissions only to the portion of CO₂ emission that excludes energy sector CO₂, i.e. agriculture, forestry and land use. Second, any assumption about the spatial and temporal variations in FFCO2 will leave a residual in the posterior solution, irrespective of the subtraction of the prior (e.g. Oda et al 2019, Wang et al 2020). It is important to note that top-down methods also suffer from their own errors, and there are still large discrepancies in posterior regional fluxes estimated by using different approaches (e.g. Peylin et al 2013, Houweling et al 2015, Takagi et al 2015, Crowell et al 2019), partially due to differences in atmospheric transport modeling (e.g. Schuh et al 2019).

In this study, we investigate how different assumptions about FFCO2 inventories, particularly temporal changes, can imprint themselves onto posterior flux estimates. For this work we use the independent ODIAC and GridFED emission inventories, which were used in the recent inversion-based inventory assessment prototyping studies, such as Deng et al (2022) and Byrne et al (2022), to help drive the GEOS-Chem model of atmospheric CO₂. We use the inventory difference as an estimate of FFCO2 errors. An established ensemble Kalman Filter (EnKF) is used to infer posterior net CO₂ fluxes from in-situ and satellite data. We describe the GEOS-Chem and its CO₂ inventories, the EnKF, and the in-situ and satellite data in next section. In section 3, we report our results and explore how differences the two FFCO2 emission inventories play a role in posterior fluxes estimates for the natural biosphere. We conclude the paper in section 4 with a broader discussion of our results and recommendations for further work.

2.1. Fossil fuel CO₂ emission datasets

2.2. Flux inversion system

2.3. Observational data

3.1. FFCO2 uncertainty challenge in flux inversions

Figure 1 shows the prior and the posterior net fluxes (fossil + land biosphere + fires + oceans) from two satellite data inversions that use different FFCO2 products (section 2.1). Results are shown for global, over aggregated continental regions (northern land and tropical land) and large source areas/countries (North America, China and Europe). We primarily focus on the land fluxes because FFCO2 plays only a small role in the size of ocean fluxes. At these large spatial scales, the differences between two sets of inversions, including prior and posterior fluxes, are small compared to the magnitude of the net prior and posterior fluxes. The difference plots of two inversions (smaller panels in figure 1) show that the seasonal amplitude of the global flux difference is ∼0.15 PgC/month, corresponding to ∼4% of the global CO₂ flux seasonal amplitude (∼3.5 PgC/month). These differences in the global fluxes are largely attributable to the emissions from the Northern Hemisphere where most of the large emitting countries, including the top emitting countries, such as China, the U.S, and India (based on Gilfillan and Marland 2021), are located (see global and North Land plots).

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These difference plots in figure 1 also illustrate the challenge of correctly prescribing a seasonal component of FFCO2. Differences introduced by competing assumptions about seasonal FFCO2 in the prior fluxes are largely eliminated in the posterior fluxes via flux optimization inversion. The posterior fluxes associated with using ODIAC are slightly larger than those that use GridFED. We find that the substantially reduced seasonal difference in net posterior fluxes is due to a compensating seasonal cycle for posterior natural fluxes (terrestrial biosphere and oceans). In short, the inversion has successfully fitted net CO₂ fluxes (the sum of fixed FFCO2 and adjusted natural fluxes) to atmospheric CO₂ concentrations by adjusting only the natural fluxes, which will potentially also include an adjustment due to an erroneous seasonal cycle for FFCO2. This misattribution of the FFCO2 seasonality to the natural fluxes is common to all the inversions we present. This misattribution error is more problematic for countries that are not spatially well-resolved by the available data the resolution of flux estimations, with the impact proportional to the magnitude of emissions, as discussed earlier. For example, 75% of the countries and territories in the world are smaller than the typical size of the land sub region in the inversion system (approximately, 500 000 km²) (https://en.wikipedia.org/wiki/List_of_countries_and_dependencies_by_area). Accurately prescribing sub-annual FFCO2 is therefore crucial to obtain robust flux estimates, especially for obtaining continental country specific emission estimates in support of inventory evaluation.

3.2. How are FFCO2 seasonal differences imprinted on net and land biosphere fluxes?

The misattribution error described above is exacerbated especially when prior FFCO2 is then subtracted from the posterior net fluxes to estimate the posterior natural fluxes, a typical approach that implicitly assumes that FFCO2 errors are much smaller than natural flux errors. Figure 2 shows the posterior natural flux maps and the difference map for boreal summer (June, July and August) and winter (December, January and February) months for both sets of inversions that use satellite and in-situ data. All the inversions use the same prior natural flux inventories, and differences in their prior FFCO2 inventories are shown in figure S1. The large spatial patterns of posterior net fluxes are similar among the cases (see panels of the top two rows in figure 2), as expected. We focus on the differences between inversions that use different FFCO2, which show the influence of assuming different FFCO2 seasonality on the posterior natural flux estimates. Noticeable differences are over the major emitting areas, including China, the U.S, and Europe, consistent with the continental-scale net fluxes (figure 1). We find that the influences of FFCO2 differences on natural fluxes are significant (∼40% of the natural portion of the net fluxes, see figure S3) on sub-continental scales.

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Comparing posterior natural fluxes inferred from satellite data (left two columns in figure 2) and in-situ data (right two columns in figure 2), we find that posterior differences are larger for the inversion that uses satellite data than the inversion that uses in-situ data over the regions where FFCO2 discrepancies are largest. This is largely because the ground-based network sites are historically (and intentionally) placed at remote geographical locations, where fossil fuel contributions are minor, to support background monitoring of atmospheric CO₂ and other gases. Thus, the posterior fluxes from in-situ inversions should be less sensitive to FFCO2 errors compared to the inversion case with satellite data because of the spatial coverage and/or density differences between two observation systems. Conversely, the in-situ inversion tends to mitigate more of the difference in FFCO2 inventories over remote areas which are poorly constrained by observations, such as central and west China. Generally, we find that satellite observations provide denser spatial coverage compared to the ground network, acknowledging that satellite data represent different information to the in-situ data, i.e. column averaged CO₂ retrieved from radiance measurements compared to CO₂ mole fractions sampled in the lower troposphere. Obtaining robust flux estimates with improved spatial resolutions requires dense CO₂ data. Satellites, such as NASA's OCO-2 and Japan's GOSAT, have collected data globally, including geographical gaps left by the ground-based global reference network.

The smaller posterior flux differences due to different assumptions about seasonal changes in FFCO2 when we use satellite data, compared to when we use in-situ data, are seemingly a welcome result. However, they also highlight the challenge of dealing with FFCO2 contributions, especially in the satellite flux inversion framework, because of the sensitivity of the observations to FFCO2. It is important to reiterate that we find that the inversion system adjusted the natural fluxes to help compensate for FFCO2 differences. It is also important to note that the flux differences between the inversions that use different FFCO2 products are still smaller than the difference between inversions that use satellite and in-situ data (see figure S4).

Figure 3 shows the posterior model CO₂ concentration differences, inferred from OCO-2 X_CO2 retrievals, resulting from using the different FFCO2 inventories. We present differences for the boundary layer and total dry-air column X_CO2 for both the winter (January, 2017) and summer (July, 2017) cases, to show the FFCO2 error sensitivity for the future space-borne and surface-based observation systems, in addition to using the current OCO-2 constraints. As expected, the impact of the FFCO2 errors are more significant near the surface and near the source regions. Some of the FFCO2 errors were not corrected even after the model had been fitted to the data (see figure S5). For example, the posterior concentration fields show 0.5 ppm differences in the boundary layer over the high northern latitudes. Historically, ground-based observations are often located far from those intense emission areas, but recent (and planned future) dense regional networks, such as Europe (Heiskanen et al 2022), North America (e.g. Karion et al 2020), and East China, can detect those differences (of up to 4 ppm) and therefore represent potentially useful constraints on local FFCO2 inventories. In contrast, X_CO2 differences are more spread out and planned satellites missions (of which the most prominent example is the upcoming Copernicus CO2 Monitoring mission, CO2M) should be able to pick up these differences and minimize the misattribution of errors in prior inventories between regions with different observation constraints. This suggests that satellite-based inversions are in a better position going forward to serve as a global tool for the QA/QC and verification due to its global dense observation coverage. Typically, the differences showed below are within the model errors assigned (for example, 1–2 ppm, Schuh et al 2019). The increased observation coverage might lead to a need for reassessing the model-observation mismatch values based on the FFCO2 differences. As seen in the flux map comparison, we find the largest differences over high-emitting areas, such as US coastal, Europe and China/India, while the differences are more confined locally in the case of boundary layer and X_CO2 differences are less pronounced and less localized over geographical region where in-situ data are particularly sparse.

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Under the Paris Agreement, new mechanisms, such as submission of NDC and the Global Stocktake (GST), are introduced to achieve the temperature goal via our global collective efforts. In addition to mandatory emission reporting to UNFCCC, each signatory country must submit a NDC that describes their GHG emission reduction goals, trajectory, and the approaches they will use to achieve that trajectory. GST is an evaluation process of our progress towards the Paris Agreement goal. GST is planned to be held every five years and the results of the assessment are used to set more stringent target in the next NDCs. Currently the very first GST is underway. In addition to the synthesis reports, such as IPCC reports, GST is the technical assessment process where science-based approaches should be fully utilized to address the guiding mitigation and adaptation questions.

While the NEIs submitted to UNFCCC remain the fundamental tool to keep track of emission changes of parties, the use of NEIs for fully addressing the mitigation guiding questions in GST is challenging. For example, NEIs might not cover all the sources and sinks that we need for global assessment using earth system models, but emissions from the key sectors for individual countries. The NEIs are specifically designed to keep track of emission changes from the countries. Depending on the data and capacity availability, estimates could be obtained with different levels of details (Tier 1–3) and thus emissions from different countries might not be comparable due to the underlying data and emission factors. While NEIs should cover key GHG emission sectors for countries, the emission might not be complete to represent all the GHG emissions from the domain for the year of interest. NEIs also do not cover emissions from international marine bunkers and aviation. Moreover, as discussed earlier, the emissions are not provided beyond country and annual scales. Thus, the global emission products have a key role in the technical assessment in GST to supplement the emission information that we cannot obtain solely from NEIs.

The use of gridded emissions allows us to perform atmospheric data-based emission analyses, such as atmospheric inversions. Several studies have reported anthropogenic emission estimates determined by inversion approaches, but these are often limited to relatively small spatial scales, such as cities and local sources (e.g. Lauvaux et al 2020). Large scale inversions, which typically estimate fluxes on spatial scales comparable to NEIs, are often done in a conservative way that avoid the direct estimation of FFCO2, with some exceptions, e.g. Maksyutov et al (2021). Consequently, the current focus of CO₂ inventory evaluation using inversions has been the Agriculture, Forestry and Other Land Use sector (e.g. Deng et al 2022, Byrne et al 2022). Our results demonstrated that inversions compensate the FFCO2 errors, but the corresponding flux corrections are attributed exclusively to the natural fluxes. To effectively evaluate NEIs using atmospheric inversions, we would need improvements to the current inversion approaches. Flux resolutions of inversions might be often too large to resolve individual countries, especially for small countries. Previous studies have examined the missing sources in many inversions, such as CO₂ from oxidation of reduced carbon species (e.g. Wang et al 2020).

To improve the ability of estimating anthropogenic emissions and other combustion emissions, such as fires, the use of multiple species should be also considered. Ultimately, this is a necessary step because reporting net fluxes of CO₂ are not enough to describe the collective assessment in a GST, especially addressing the guiding questions. Effective mitigation of national emissions of anthropogenic GHGs requires reliable knowledge of emissions from individual contributing sectors. Sector emissions of CO₂ are typically accompanied by a range of trace gases that are typically measured by the air quality (AQ) community, some of which are also observed by Earth-observing satellites, e.g. carbon monoxide and nitrogen dioxide that are used commonly as tracers for incomplete combustion. A synergy of GHG and AQ measurements is there important to support the mitigation of GHG emissions, including at least better coordination of GHG and AQ measurement networks. The U.S. and Europe have extensive ground-based observation networks (e.g. NOAA and ICOS) and some of the sites have been used to study FFCO2 (e.g. Basu et al 2020). We also need to improve modeling of atmospheric transport (Simmonds et al 2021) and chemistry to help reduce the uncertainties associated atmospheric transport that are often the dominant error component in inversions (e.g. Schuh et al 2019).

Ideally, GHG inventories should be developed in a way to fully utilize the model and observations. Given the timeline of UNFCCC framework, the efforts made by the scientific inventory community will help fill the knowledge gaps and guide the framework to be more responsive to the evolving needs of climate mitigation. We argue that an extended data collection would greatly help improving the utility of inversions. For example, the use of the subnational data as noted by IPCC (2019) is optional, but it is an effective way to improve the description of emissions in space and time. As we showed in our study, obtaining robust seasonal emission estimates should directly improve the accuracy of inversion results especially reducing the impact of large emitting countries. The availability of the activity data for emission calculation at subnational scales, especially cities, could be limited and the robustness of the system boundary calculation is lower in theory.

Temporal emission disaggregation is challenging due to the limited data availability. Andres et al (2011) was based on the fuel data collected from the top 20 emission countries. The uncertainty associated with the temporal component was about 15%–20%. Beyond monthly scales, there are not many options for us to implement downscaling (e.g. Nassar et al 2013, Crippa et al 2020). The use of alternative activity data has emerged (e.g. Le Quéré et al 2020, Liu et al 2020), but the accuracy of the resulting emissions are not fully evaluated. The expected uncertainty should be much higher than what we typical expected from inventory estimates based on fuel consumption (Oda et al 2021). The incremental approach is suitable for near-real time (NRT), but it does not provide total constrain and thus could be biased (see figure S6). For example, most of the emissions in NRT CO₂ emissions were represented by US and China data where emission calculations were well supported by statistical data. For these reasons, an established framework could take a role as clearing house to coordinate data collection for NEIs and GST. Looking ahead, capacity building for the development of reliable inventories in the projected large emitting countries is important.

We examined the impact of the FFCO2 errors on the flux inversion results using two observation systems. We revisited the FFCO2 assumption, one of the obstacles in the conventional flux inversion for serving as a tool for QA/QC and evaluation/variation of reported NEIs as well as potentially providing GHG estimates for countries with less robust inventory capacity and examined the impact of the inverse estimates using two inventories that approximate FFCO2 errors. We demonstrated how FFCO2 errors can cause biases in posterior flux estimates. The magnitude of the errors are small compared to the magnitude of natural fluxes and on national scales but can be significant on subnational scales. We found that differences in the prior seasonal differences in FFCO2 are the largest driver for the estimation of natural fluxes. We found that errors associated with prescribing seasonal emissions are larger and more direct than errors associated with prescribing the spatial distribution of emissions. For the use of inversions for inventory evaluation, we need robust sub-annual estimates for FFCO2, especially for large emitting countries such as China, to quantify robust top-down emission estimates, particularly at policy-relevant national and subnational scales. Extended data collection would directly improve accuracy of inverse estimates for science and global monitoring of GHG emissions under the Paris Agreement.

We found that satellite data provide us with the best opportunity to quantify FFCO2 emission errors; a similar result is achievable using dense, regional in-situ measurement networks. Therefore, they provide a better option to evaluate national emission inventories. However, the corresponding top-down flux corrections associated with errors in FFCO2 are attributed to natural flux estimates by virtue of a common approach adopted by inverse methods, which implicitly assumes that we have perfect knowledge of FFCO2. To help improve the evaluation of NEIs and the technical assessment in the GST, inversions need to improve the accuracy of their estimates and to improve knowledge of the processes that explain the difference between models and atmospheric data, e.g. emissions, atmospheric transport.

T O is supported by NASA Grant # 80NSSC21K1929. L F and P I P acknowledge support from the UK National Centre for Earth Observation funded by the Natural Environment Research Council (NE/R016518/1). Authors acknowledge contribution of the following invividuals to the ObsPack CO₂ GLOBALVIEWplus product (v7.0): Kenneth N Schuldt, John Mund, Ingrid T Luijkx, Tuula Aalto, James B Abshire, Ken Aikin, Arlyn Andrews, Shuji Aoki, Francesco Apadula, Bianca Baier, Peter Bakwin, Jakub Bartyzel, Gilles Bentz, Peter Bergamaschi, Andreas Beyersdorf, Tobias Biermann, Sebastien C Biraud, Harald Boenisch, David Bowling, Gordon Brailsford, Gao Chen, Huilin Chen, Lukasz Chmura, Shane Clark, Sites Climadat, Aurelie Colomb, Roisin Commane, Sébastien Conil, Adam Cox, Paolo Cristofanelli, Emilio Cuevas, Roger Curcoll, Bruce Daube, Kenneth Davis, Martine De Mazière, Stephan De Wekker, Julian Della Coletta, Marc Delmotte, Joshua P DiGangi, Ed Dlugokencky, James W Elkins, Lukas Emmenegger, Shuangxi Fang, Marc L Fischer, Grant Forster, Arnoud Frumau, Michal Galkowski, Luciana V Gatti, Torsten Gehrlein, Christoph Gerbig, Francois Gheusi, Emanuel Gloor, Vanessa Gomez-Trueba, Daisuke Goto, Tim Griffis, Samuel Hammer, Chad Hanson, László Haszpra, Juha Hatakka, Martin Heimann, Michal Heliasz, Arjan Hensen, Ove Hermanssen, Eric Hintsa, Jutta Holst, Viktor Ivakhov, Dan Jaffe, Warren Joubert, Anna Karion, Stephan R Kawa, Victor Kazan, Ralph Keeling, Petri Keronen, Pasi Kolari, Katerina Kominkova, Eric Kort, Elena Kozlova, Paul Krummel, Dagmar Kubistin, Casper Labuschagne, David H Lam, Ray Langenfelds, Olivier Laurent, Tuomas Laurila, Thomas Lauvaux, Jost Lavric, Bev Law, Olivia S Lee, John Lee, Irene Lehner, Reimo Leppert, Markus Leuenberger, Ingeborg Levin, Janne Levula, John Lin, Matthias Lindauer, Zoe Loh, Morgan Lopez, Toshinobu Machida, Ivan Mammarella, Giovanni Manca, Andrew Manning, Alistair Manning, Michal V Marek, Melissa Y Martin, Hidekazu Matsueda, Kathryn McKain, Harro Meijer, Frank Meinhardt, Lynne Merchant, N Mihalopoulos, Natasha Miles, Charles E Miller, John B Miller, Logan Mitchell, Stephen Montzka, Fred Moore, Eric Morgan, Josep-Anton Morgui, Shinji Morimoto, Bill Munger, David Munro, Cathrine L Myhre, Meelis Mölder, Jennifer Müller-Williams, Jaroslaw Necki, Sally Newman, Sylvia Nichol, Yosuke Niwa, Simon O'Doherty, Florian Obersteiner, Bill Paplawsky, Jeff Peischl, Olli Peltola, Salvatore Piacentino, Jean M Pichon, Steve Piper, Christian Plass-Duelmer, Michel Ramonet, Ramon Ramos, Enrique Reyes-Sanchez, Scott Richardson, Haris Riris, Pedro P Rivas, Thomas Ryerson, Kazuyuki Saito, Maryann Sargent, Motoki Sasakawa, Daniel Say, Bert Scheeren, Tanja Schuck, Marcus Schumacher, Thomas Seifert, Mahesh K Sha, Paul Shepson, Michael Shook, Christopher D Sloop, Paul Smith, Martin Steinbacher, Britton Stephens, Colm Sweeney, Pieter Tans, Kirk Thoning, Helder Timas, Margaret Torn, Pamela Trisolino, Jocelyn Turnbull, Kjetil Tørseth, Alex Vermeulen, Brian Viner, Gabriela Vitkova, Stephen Walker, Andrew Watson, Steve Wofsy, Justin Worsey, Doug Worthy, Dickon Young, Sönke Zaehle, Andreas Zahn, Miroslaw Zimnoch, Alcide G di Sarra, Danielle van Dinther, Pim van den Bulk.

All data that support the findings of this study are included within the article (and any supplementary files). The ODIAC data product is available from https://db.cger.nies.go.jp/dataset/ODIAC/. The GCP-GridFED data product can be obtained from https://zenodo.org/record/3958283#.ZCmkCOzMKrN. The OCO data product used in this study is available from NASA's Goddard Earth Sciences Data and Information Services Center (GES DISC, https://disc.gsfc.nasa.gov/). The GLOBALVIEWplus CO₂ product is available from NOAA's Global Monitoring Laboratory website (https://gml.noaa.gov/ccgg/obspack/our_products.php). The model results are available upon reasonable request.

T O and P I P conceived the study. T O developed the ODIAC data product. L F performed the inversion analysis. T O wrote the initial manuscript based on the input from all authors. All authors contributed to the interpretation of the analysis and discussion. All authors read and approved the final manuscript