Yaniv Brandvain
email: ybrandvain@gmail.com

Genomic parallelism in adaptation to orthogonal environments in sea horses

de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

A recommendation of

  Riquet F, Liautard-Haag C, Woodall L, Bouza C, Louisy P, Hamer B, Otero-Ferrer F, Aublanc P, Beduneau V, Briard O, El Ayari T, Hochscheid S, Belkhir K, Arnaud-Haond S, Gagnaire PA, and Bierne N. Parallel pattern of differentiation at a genomic island shared between clinal and mosaic hybrid zones in a complex of cryptic seahorse lineages. bioRxiv, 161786 ver. 4 peer-reviewed and recommended by PCI Evol Biol (2017) Studies in speciation genomics have revealed that gene flow is quite common, and that despite this, species can maintain their distinct environmental adaptations. Although researchers are still elucidating the genomic mechanisms by which species maintain their adaptations in the face of gene flow, this often appears to involve few diverged genomic regions in otherwise largely undifferentiated genomes. In this preprint [1], Riquet and colleagues investigate the genetic structuring and patterns of parallel evolution in the long-snouted seahorse. Before investigating specific SNPs plausibly associated with adaptation, the authors first describe genome-wide population structure in the long-snouted seahorse. This species is split into five phenotypically similar, but genetically distinct populations. Two populations reside in the Atlantic Ocean and are geographically structured with one north of the Iberian peninsula and the other around the Iberian peninsula. Two other populations are found in the Mediterranean Sea and are structured by the environment as they correspond to marine and lagoon environments. The genetic clustering of lagoon populations in the Mediterranean, despite the substantial geographic distance between them is quite impressive, and worthy of further study. Finally, a fifth population resides in a lagoon-like habitat in the Black Sea. The authors then investigate patterns of extreme genomic differentiation among populations, and uncover a remarkable pattern of parallel differentiation in these populations. In an PEER COMMUNITY IN EVOLUTIONARY BIOLOGY | DOI: 10.24072/pci.evolbiol.100056 1 of 2

outlier scan, Riquet and colleagues find numerous SNPs in one genomic region that separates northern and southern Atlantic populations. Quiet surprisingly, this same genomic region appears to differentiate populations living in marine and lagoon habitats in the Mediterranean. The idea that parallel patterns of genomic differentiation may underlie adaptation to differing environmental scenarios has not yet received much attention. This paper should change that.

This paper is particularity impressive in that the authors uncovered this intriguing pattern with under three hundred SNPs. Future genome scale studies will uncover the genomic basis behind this unusual case of parallelism.

Appendix


Antoine Miné
email: antoine.mine@lip6.fr

Matthieu Journault
email: matthieu.journault@lip6.fr

Design of a Modular Platform for Static Analysis

Keywords: Static analysis, Abstract interpretation, Tool Acknowledgments

published or not. The documents may come

Introduction

Abstract interpretation [START_REF] Cousot | Abstract Interpretation: A Unified Lattice Model for Static Analysis of Programs by Construction or Approximation of Fixpoints[END_REF], a theory of the approximation of semantics, allows designing sound static analyzers that infer automatically program properties. It has enjoyed a growing success, as witnessed by commercial tools used in the industry: Polyspace Verifier, Astrée [START_REF] Kästner | Astrée: Proving the absence of runtime errors[END_REF], Sparrow [START_REF] Oh | Design and Implementation of Sparse Global Analyses for C-like Languages[END_REF], Julia [START_REF] Spoto | JULIA: A Generic Static Analyser for the Java Bytecode[END_REF], etc. Open-source industrial-strength frameworks to design analyzers by abstract interpretation have also been proposed: Frama-C [START_REF] Cuoq | Frama-C: A software analysis perspective[END_REF], IKOS [START_REF] Brat | IKOS: A Framework for Static Analysis Based on Abstract Interpretation[END_REF], Infer [START_REF] Calcagno | Moving Fast with Software Verification[END_REF], etc. Most tools focus on analyzing families of C-like or Java-like languages, and do not target dynamic languages (e.g., Python, JavaScript) and a forciori cannot handle both kinds of languages. Moreover, while all tools are based on a modular combination of abstractions, as advocated by abstract interpretation [START_REF] Cousot | Systematic design of program analysis frameworks[END_REF], these are often restricted to specific abstractions: e.g., Astrée [START_REF] Cousot | Combination of abstractions in the Astrée static analyzer[END_REF] achieves a reduced product of numeric abstractions but has a monolithic memory abstraction; Frama-C's abstractions can be composed either through coarse-grain plug-ins, or as nonrelational value abstractions [START_REF] Blazy | Structuring Abstract Interpreters Through State and Value Abstractions[END_REF]. To try and address these TAPAS'18, August 28, 2018, Freiburg im Breisgau, Germany 2018.

issues, and push abstract interpretation frameworks further, we have started the design of a Modular Open Platform for Static Analysis (Mopsa) in OCaml. It is based on a standard interpreter by induction on the syntax and a collection of abstractions (see, e.g., [START_REF] Bertrane | Static Analysis and Verification of Aerospace Software by Abstract Interpretation[END_REF]) but with unique features: all domains share a common extensible Abstract Syntax Tree datatype; it can express both high-level syntax close to the source languages, and simpler intermediate ones used internally by abstractions (e.g., numeric fragments); we eschew static simplifications common to frameworks (e.g., LLVM [START_REF] Lattner | LLVM: A Compilation Framework for Lifelong Program Analysis & Transformation[END_REF]); transformations are performed dynamically during interpretation and benefit from inferred facts; all domains share a common interface and are easy to compose; notably, iterators are viewed as domains, and domains are responsible for statement simplification; domains need only handle a fragment of the AST; they can be reused after extending the AST to new languages. Mopsa is a work in progress: its architectural foundations are implemented, but it is not ready to analyze realistic programs. As a proof of concept, we have implemented analyses for both a fragment of C and Python, showing it can support legacy abstractions (e.g., numeric domains, low-level C memory models [START_REF] Miné | Field-sensitive value analysis of embedded C programs with union types and pointer arithmetics[END_REF]) and is a great help developing novel ones (e.g., modular C analysis [START_REF] Journault | Modular static analysis of string manipulations in C programs[END_REF], Python analysis [START_REF] Fromherz | Static value analysis of Python programs by abstract interpretation[END_REF]). Sections 2 and 3 present the domain signature and domain composition; Sect. 4 reports on early experiments (analyzing part of Juliet for C and Python's regression tests); Sect. 5 concludes.

Unified Domains Signature

Abstract domains are OCaml modules implementing the DOMAIN signature in Fig. 1. In the following, we describe the main types and functions, and state the core design goals.

Lattice. Each domain defines a type t characterizing its abstract state, as well as corresponding lattice operators (join, widening, etc.). In Mopsa, the internal abstract state of a domain is private: other domains have no direct access. This separation ensures a low coupling between domains.

Managers.

During the analysis of one statement, a domain may require computing the post-condition of statements handled by other domains. To allow inter-domain communication without sacrificing modularity, each domain transfer function is not defined over its private type t, but on the product of types from all domains. To ensure that each domain can be programmed independently from the others, the val exec : stmt -> ('a, t) man -> 'a flow -> 'a post option val eval : expr -> ('a, t) man -> 'a flow -> 'a evals option val ask : 'r query -> ('a, t) man -> 'a flow -> 'r option (* Interface *) val exec_interface : zone interface val eval_interface : (zone * zone) interface end product is a type parameter 'a, and we use an encoding of polymorphic records in OCaml: the manager ('a, t) man is a record providing lattice operators on 'a, transfer functions over all domains in 'a, and accessor functions get: 'a -> t and set: t -> 'a -> 'a to allow a domain to access and update its private abstraction within the global abstraction.

Flows. Mopsa operates by induction on the syntax of the program. To handle non-local control flows, we use continuations (similarly to Astrée [START_REF] Bertrane | Static Analysis and Verification of Aerospace Software by Abstract Interpretation[END_REF]): we collect not only environments reaching the current program location, but also those at previously encountered jump locations. Suspended flows are merged back into the current flow when reaching the corresponding jump target. Expressing flows as continuations makes it possible to abstract very complex non-local control, such as generators in Python [START_REF] Fromherz | Static value analysis of Python programs by abstract interpretation[END_REF]. Flow continuations are implemented as maps from flow tokens into the global abstraction 'a. Tokens belong to an extensible type, thus allowing a domain to add new control flow abstractions independently from the remaining domains.

Example 2.1. We give in Fig. 2 an example of a transfer function for handling forward goto statements in C. Flows are enriched with a new token T_goto annotated with the target label. When reaching a statement goto label, the current environments are moved to token T_goto label, before being reset to ⊥ because the next control location becomes unreachable. Encountering label: stmt merges environments associated to T_goto label into current environments, and returns a post-condition of stmt via the manager. The default case returns None, indicating that other domains should handle the other constructions. Such a pure iterator domain does not maintain any abstract state by itself, hence t = unit. Despite its brevity, the code in Fig. 2 analysis. It is completely decoupled from other domains, and thus highly reusable.

Evaluations. Domains in Mopsa can implement dynamic rewriting rules to simplify expressions by exploiting the available abstract information. A classic use is transforming modular arithmetic from C expressions into mathematical arithmetic, easier to handle in relational numeric domains, after ensuring the absence of overflows in the current state.

After a statement or expression is transformed by one domain, it is executed again via the manager on all existing domains. We must take care to avoid infinite rewriting loops. Mopsa introduces the notion of zones to avoid this problem. Zones define (possibly overlapping) AST fragments, such as expressions with modular arithmetic or purely mathematical expressions. When adding a new language, the extensible type Zone.t of zones can be enriched along with the extensible type of statements and expressions. Calls to transfer functions and rewriting tag input and output AST with zone information, and the manager routes the calls accordingly to relevant domains. It is then easy to ensure that abstract computations and rewriting progress until completion.

Another contribution of Mopsa is the ability to handle natively disjunctive evaluations. Domains can return different results for different parts of the input abstract environment. Consider the following example from Python analysis: Example 2.2. Fig. 3 shows the evaluation of an index access on Python lists. We assume that lists are abstracted with summary and length variables over-approximating the contents and the number of elements, as done in [START_REF] Fromherz | Static value analysis of Python programs by abstract interpretation[END_REF]. When analyzing a read access, the function getitem_cases is used to partition the pre-condition w.r.t. the length. The first flow flow1 represents the case when index i is outside the size of self. The associated evaluation is an empty expression since an exception is raised. The second flow flow2 is obtained by filtering the pre-condition verifying that the list contains exactly one element. In this case, the summary variable is returned as a sound simplification of index access. Finally, when the list contains at least two elements, a temporary variable is created as a copy of the summary variable using the expand function, similarly to the case of summarized arrays [START_REF] Gopan | Numeric Domains with Summarized Dimensions[END_REF]. With the expression, a cleaning function is returned that will be called to remove the temporary variable once all rewritings are done.

Queries. When a domain needs specific information maintained by another domain, it can fetch them via queries, similarly to Astrée [START_REF] Cousot | Combination of abstractions in the Astrée static analyzer[END_REF]. The type _ query is an extensible public GADT type that can be enriched by domains. For example, an interval query can be defined by: type _ query += Q_interval: expr -> Itv.t query Numeric domains handle requests to Q_interval in the transfer function ask, and client domains retrieve this information via their manager by calling man.ask (Q_interval e) flow. GADT typing ensures that the returned value has type Itv.t.

Domain Composition

The global abstraction of an analysis instance is constructed at run-time by composing domains according to a user-given configuration file. An illustrative example is depicted in Fig. 4 representing a simplified version of an analysis of C. Three types of generic composers are used to connect leaf domains:

Iterators. This composer iterates sequentially over a set of domains, which is materialized with in Fig. 4. Lattice operators are defined pointwise, and transfer functions are called in sequence until one succeeds: domain i is invoked only if previous domains j < i returned None. This composition is useful to combine a set of iterators defining transfer functions for disjoint parts of the AST, such as loops, function calls, etc. In addition, it allows plugging new iteration schemes easily, e.g., replacing the induction-based iterators with CFG-based ones.

Reduced products. The classic method employed in most static analyzers (e.g., [START_REF] Bertrane | Static Analysis and Verification of Aerospace Software by Abstract Interpretation[END_REF]) for creating reduced products is via cascading binary functors. Mopsa provides instead a generic n-ary reduced product composer that enables better propagation of reduction channels. Lattice operators are defined pointwise and transfer functions of argument domains are called in parallel. All post-conditions are given to a userdefined reduction operator, that can access directly abstract elements of any domain in the pool and can exploit the published reduction channels to refine the final post-condition.

Stacks. Another novelty in Mopsa is a stacked reduced product of n functors sharing the same subordinate domain instance. This form of composition is useful when several domains depend on an external domain to delegate management of parts of their abstract state. Consider the case of cell and smashing abstractions from [START_REF] Bertrane | Static Analysis and Verification of Aerospace Software by Abstract Interpretation[END_REF][START_REF] Miné | Field-sensitive value analysis of embedded C programs with union types and pointer arithmetics[END_REF] in Fig. 4. Both domains need a pointer domain for address resolution and a numeric domain for abstracting numeric environments. By sharing the same numeric domain instance, relations between cells and smashed variables can be inferred.

Experiments

We instantiated two analyzers, one for C (Fig. 4) and one for Python (Fig. 5). We note that the configurations share several domains (underlined), including iterators, heap and numeric abstractions. C benchmarks were taken from the Juliet Test Suite (v 1.3) for C/C++. We selected all the C tests corresponding to the following categories: CWE190 on integer overflows, CWE369 on divisions by zero, and CWE476 on null pointer dereferences. Each category provides several test cases, themselves split in two programs: a bad program containing an error, and its corrected version. Python benchmarks were performed on regression tests from the official Python 3.6.3 distribution, that test the builtins of the language and the standard library. The current configuration for the Python analysis does not provide an analyzer able to handle all the 500 regression tests; we selected 9 tests in the scope of our configuration (see [START_REF] Fromherz | Static value analysis of Python programs by abstract interpretation[END_REF] for more information). Tables 1 and2 provide results of these experimentations: ✓ are good programs for which no alarm was raised, ✓ are bad programs for which an alarm was raised, ✗ are good programs for which the analyzer raised an alarm (false positive), ✱ are programs that could not be handled by the analyzer (e.g., by lack of stubs). False positives in CWE369 are due to the use of a non-partitioned numerical domain for the analysis of programs testing divisions by zero; thanks to the modularity of the analyzer, this could be avoided by adding a partitioning domain.

Figure 1 .

 1 Figure 1. Unified signature for abstract domains.

  is the complete transfer function of a domain that adds C-style forward goto to an type token += T_goto of Ast.label let exec stmt man flow = match stmt with | S_c_goto(label) -> (* Case of S ♯ goto label *) let cur_env = Flow.find T_cur man flow in let flow' = Flow.add (T_goto label) cur_env man flow in let flow'' = Flow.set T_cur man.bottom man flow' in Post.return flow'' | S_c_label(label, stmt) -> (* Case of S ♯ label: stmt *) let goto_env = Flow.find (T_goto label) man flow in let flow' = Flow.add T_cur goto_env man flow in let flow'' = man.exec stmt flow' in Post.return flow'' | _ -> None

Figure 2 .

 2 Figure 2. Transfer function for forward goto statements.

(

  * Case of E ♯ list.__getitem__(self, i) *) let flow1, flow2, flow3 = getitem_cases self i man flow in let evl1 = let flow' = man.exec (mk_raise "IndexError") flow1 in Eval.empty flow' in let evl2 = Eval.singleton (summary self) flow2 in let evl3 = let tmp = mk_tmp () in let flow' = man.exec (expand tmp (summary self)) flow3 in Eval.singleton tmp flow' ~cleaner:[remove_var tmp] in Eval.or_list [evl1; evl2; evl3]

Figure 3 .

 3 Figure 3. Evaluation of index access on lists in Python.

Table 1 .

 1 We have presented the design principles of Mopsa, a new platform for static analysis development through compositions of highly reusable abstractions. It is not yet featurecomplete, but it is already successfully used in research projects to support the analysis of non-trivial C and Python codes[START_REF] Fromherz | Static value analysis of Python programs by abstract interpretation[END_REF][START_REF] Journault | Modular static analysis of string manipulations in C programs[END_REF]. In the future, we plan to extend the support for C standard libraries and Python built-ins to be able to analyze realistic codes. Other research projects on Mopsa include static analysis of novel properties beyond safety, such as a portability analysis. We plan to release Mopsa as open-source. Benchmarks on regression tests of Python 3.6.

	C program	C libs	C desugarisation
	C switch C interproc	loops	Regression test test_augassign	Lines Tests Time ✓ ✗ ✱ Coverage 273 7 645ms 4 2 1 85.71%
					test_baseexception	141	10	20ms	6 0 4	60.00%
	intraproc	interproc	C goto	test_bool	294	26	47ms 12 0 14	46.15%
					test_builtin	454	21	360ms 3 0 18	14.29%
					test_contains	77	4	418ms 1 0 3	25.00%
		heap			test_int_literal	91	6	29ms	6 0 0	100.00%
					test_int	218	8	88ms	3 0 5	37.50%
	C cells	×	C smash		test_list test_unary	106 39	9 6	88ms 11ms	3 0 6 2 0 4	33.33% 33.33%
		C integers		Total	1693	97	1.71s 40 2 55	43.30%
	C pointers
			boxes
	Leaf domains	Functor domains	Iterator composer
	Product composer	Stack composer
	Figure 4. C analysis configuration.
	5 Conclusion and Future Work
	Py program	Py libs	Py desugarisation
	Py exceptions Py generator	intraproc
	interproc	loops	Py objects
	Py containers Py data model	heap
			boxes
	Figure 5. Python analysis configuration.

Table 2 .

 2 Benchmarks on CWE from the Juliet test suite.

	tests	Loc Tests	Time	✓	✓	✗	✱	Coverage
	CWE190 440k 6840 11.0mn 2584 3213 0 1043	84.75%
	CWE369 109k 1368 3.30mn	76	380 304 608	55.55%
	CWE476 25k	522 0,207mn 270 252	0	0	100%
	Total	574k 8730 14.5mn 2930 3845 304 1651	77.60%

This work is partially supported by the European Research Council under Consolidator Grant Agreement 681393 -Mopsa.


Graeme L Stephens
email: graeme.stephens@jpl.nasa.gov

Bruno Christophe
email: bruno.christophe@onera.fr

Alfred E Nash
email: alfred.e.nash@jpl.nasa.gov

Bernard Foulon
email: bernard.foulon@onera.fr

Byron D Tapley
email: tapley@csr.utexas.edu

Frank H Webb
email: frank.h.webb@jpl.nasa.gov

Maria Z Hakuba
email: maria.z.hakuba@jpl.nasa.gov

Srinivas V Bettadpur
email: srinivas@csr.utexas.edu

Earth's Energy Imbalance measured from Space

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) <

Abstract-The direct measurement of Earth's energy imbalance (EEI) is one of the greatest challenges in climate research. The global mean EEI represents the integrated value of global warming and is tightly linked to changes in hydrological cycle and the habitability of our planet. Current space-born radiometers measure the individual radiative components of the energy balance with unprecedented stability, but with calibration errors too large to determine the absolute magnitude of global mean EEI as the components' residual. Best estimates of long-term EEI are currently derived from temporal changes in ocean heat content at ~0.7 Wm -2 . To monitor EEI directly from space, we propose an independent approach based on accelerometry that measures nongravitational forces, such as radiation pressure, acting on Earth orbiting spacecrafts. The concept of deriving EEI from radiation pressure has been considered in the past, and we provide analysis that shows today's capabilities are sufficiently accurate to answer the question: At what rate is our planet warming? To measure global mean EEI to within at least ±0.3 Wm -2 requires spacecraft(s) of near-spherical shape and well-characterized surface properties to reduce confounding effects. The proposed concept may provide the basis for a data record of global and zonal mean EEI on annual and potentially monthly time scales. It is not meant to replace existing concepts designed to measure energy balance components or ocean heat storage, but to complement these by providing an independent estimate of EEI for comparison and to anchor data products and climate models that lack energy balance closure. BACKGROUND THE Earth's global mean energy imbalance (EEI) and its temporal variability is the most direct measure of the magnitude and change of global warming [START_REF] Von Schuckmann | An imperative to monitor Earth's energy imbalance[END_REF][2] [START_REF] Cheng | Taking the pulse of the planet[END_REF]. Presently, two predominant ways are pursued to estimate the build-up of heat in our climate system. The first deduces the imbalance as a residual of the sum of the individual fluxes of incoming and outgoing shortwave and longwave radiation at the top-of-theatmosphere (TOA). The second approach infers the EEI as the temporal change in ocean heat content derived either from insitu profiles of ocean temperature, such as measured by Argo's automated floats [START_REF] Gould | Argo profiling floats bring new era of in situ ocean observations[END_REF] [START_REF] Riser | Fifteen years of ocean observations with the global Argo array[END_REF], from ocean modeling and reanalysis [START_REF] Balmaseda | The Ocean Reanalyses Intercomparison Project (ORA-IP)[END_REF] [START_REF] Palmer | Ocean heat content variability and change in an ensemble of ocean reanalyses[END_REF], or from combinations of remote sensing techniques [8] [9]. Ninety-three percent of the excess heat due to global warming is stored in the world's oceans [START_REF] Rhein | Observations: Ocean[END_REF], buffering the temperature increase at Earth's land surface and atmosphere. The retrieval of ocean heat storage (i.e. temporal change in ocean heat content) from Argo and historical in-situ measurements [START_REF] Abraham | A review of global ocean temperature observations: Implications for ocean heat content estimates and climate change[END_REF] [START_REF] Cheng | Improved estimates of ocean heat content from 1960 to 2015[END_REF] is considered the most reliable source for global mean EEI over the past decades [START_REF] Rhein | Observations: Ocean[END_REF] [13][14], ranging between 0.5 -0.9 Wm -2 (e.g. [START_REF] Hansen | REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER[END_REF][16] [START_REF] Abraham | A review of global ocean temperature observations: Implications for ocean heat content estimates and climate change[END_REF][17] [START_REF] Stephens | The Curious Nature of the Hemispheric Symmetry of the Earth's Water and Energy Balances[END_REF] [START_REF] Willis | Interannual variability in upper ocean heat content, temperature, and thermosteric expansion on global scales[END_REF]). The most reliable measurement of the radiative components of Earth's energy balance at TOA are provided by the Clouds and the Earth's Radiant Energy System (CERES [START_REF] Loeb | Observed changes in top-of-the-atmosphere radiation and upper-ocean consistent within uncertainty[END_REF]). The radiometric monitoring of the shortwave and longwave fluxes is achieved within error bounds an order of magnitude larger than the estimated global mean EEI [START_REF] Stephens | An update on Earth's energy balance in light of the latest global observations[END_REF] [START_REF] Palmer | Reconciling Estimates of Ocean Heating and Earth's Radiation Budget[END_REF]. Due to mainly calibration errors, the long-term (2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015) global mean EEI derived from CERES data is at about +4 Wm -2 [START_REF] Loeb | Toward Optimal Closure of the Earth's Top-of-Atmosphere Radiation Budget[END_REF] [START_REF] Loeb | Clouds and the Earth's Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) Top-of-Atmosphere (TOA) Edition 4.0 Data Product[END_REF] almost ten times greater than the ocean heat storage estimates from ocean in-situ measurements (see above). CERES provides an energy balanced data product (EBAF), in which the global multiannual mean fluxes are adjusted within their range of uncertainty to agree with the global long-term mean ocean heat storage [START_REF] Loeb | Toward Optimal Closure of the Earth's Top-of-Atmosphere Radiation Budget[END_REF]. This adjusted, energy-balanced data product is widely used by the community despite the lack of absolute accuracy. Although anchored to the long-term mean of global ocean heat storage, the interannual variability in CERES's EEI is independent of the ocean data and known to within ±0.3 Wm - 2 [START_REF] Loeb | Toward Optimal Closure of the Earth's Top-of-Atmosphere Radiation Budget[END_REF]. Information on temporal variability in global mean ocean heat storage from Argo is limited to decadal scale averages within about ±0.1 Wm -2 [START_REF] Von Schuckmann | An imperative to monitor Earth's energy imbalance[END_REF] [START_REF] Johnson | Improving estimates of Earth's energy imbalance[END_REF] due to presumably sampling caveats. The Argo system's spatial coverage varies over time, does not capture the deep ocean below 2000 meters, and under samples polar oceans and marginal seas. Consequently, the interannual variability derived from Argo is somewhat noisy and disagrees with the CERES EBAF record [START_REF] Trenberth | Insights into Earth's Energy Imbalance from Multiple Sources[END_REF][26] [START_REF] Trenberth | Earth's Energy Imbalance[END_REF] as also demonstrated in Figure 1 (see section II). In addition to the in-situ profiling of ocean temperature, there are two other ways to estimate the ocean heat content: ocean > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < reanalysis/models that augment the horizontal and vertical coverage [START_REF] Balmaseda | The Ocean Reanalyses Intercomparison Project (ORA-IP)[END_REF] [START_REF] Palmer | Ocean heat content variability and change in an ensemble of ocean reanalyses[END_REF], and remote sensing of ocean mass and sea level height [START_REF] Chambers | Observing seasonal steric sea level variations with GRACE and satellite altimetry[END_REF] [START_REF] Feng | Global sea level variations from altimetry, GRACE and Argo data over 2005-2014[END_REF]. A combination of such datasets, as for example originating from GRACE (ocean mass [START_REF] Tapley | GRACE measurements of mass variability in the Earth system[END_REF]) and JASON (ocean altimetry [START_REF] Leuliette | Integrating Jason-2 into a Multiple-Altimeter Climate Data Record[END_REF]), permits an estimate of global mean thermosteric sea level rise and therefore the thermal expansion of the oceans due to heat uptake. Recent literature suggests that this retrieval of global mean ocean heat storage is possible with an absolute accuracy superior to the broadband radiometry approach, whereby the magnitude and source of error are yet subjects of research (e.g., [START_REF] Jayne | Observing ocean heat content using satellite gravity and altimetry[END_REF][32] [33][34]). To date, the only way to estimate the absolute magnitude of long-term global mean EEI is via in-situ sampling or remote sensing of ocean heat storage, while the radiometric measurement provides the most viable means to monitor temporal changes in EEI. Although complementing each other, these independent approaches do not allow for intercomparison and validation. Therefore, unknown biases and uncertainties in either method cannot be precluded. Here, we present an independent approach to directly measure EEI from space that is based on the principle of measuring radiation pressure force exerted on Earth orbiting spacecrafts. The trajectory of the spacecraft(s) draws a "virtual" sphere around the Earth at orbit altitude. The objective of the mission is to obtain the net radiative flux through this sphere, through measuring the radial component of the radiation pressure acceleration the spacecraft is subjected to. This measurement has the potential to achieve an absolute accuracy well beyond what can be achieved by radiometry. Therefore, we conceive it to be an adjunct to the radiometric measurements that provide essential information about the radiative components and associated feedbacks, but cannot provide a direct measure of global mean EEI. To fill this gap, the foremost goal of the proposed concept is to provide the integrated value of global mean EEI at annual time scales. This independent estimate of the absolute magnitude of EEI can be used to anchor other datasets, such as from radiometry or climate modeling [START_REF] Mauritsen | Tuning the climate of a global model[END_REF] [START_REF] Hourdin | The Art and Science of Climate Model Tuning[END_REF], that lack energy balance closure. The secondary goal is to obtain monthly and zonal averages, providing the means to track large-scale heat transports across latitudes over seasonal and interannual timescales, and to conduct valuable inter comparisons with other independent EEI estimates originating from radiometry, ocean heat uptake, and reanalysis. In this concept, an accelerometer on board a small satellite, as widely employed to estimate non-gravitational forces in orbit, is considered a wide field-of-view (WFOV) sensor. The spacecraft's skin coating represents the sensitive area by which the radiation fluxes are transformed into forces and accelerations. It should be noted that this relatively simple technique has some important limitations, since little information can be provided on the spectral distribution, space and time resolution, and the individual radiative flux components. Deriving the radiative components from the radiation pressure approach is not per se impossible, but will not be discussed here. On satellite systems that aim at measuring very small fluctuations in Earth's gravity field at high accuracy such as GRACE or GOCE [37], ultra-sensitive accelerometers are used to quantify and eliminate the impact of non-gravitational forces such as those exerted by radiation pressure or atmospheric drag. By minimizing the non-gravitational forces other than radiation pressure through an optimal mission design, the EEI is in principle derivable within established accuracy requirements. The feasibility of this concept has been demonstrated in the past with measurements performed by the CACTUS accelerometer on CASTOR in 1975 (e.g., [START_REF] Boudon | Measurement of the radiation pressure by accelerometry: A new way to the determination of the Earth radiation budget. Result obtained with CASTOR/CACTUS experiment[END_REF]). A second ESA project, BIRAMIS, facilitated the study of a more optimized system as well as the evaluation of its error budget [START_REF] Mainguy | Biramis --Evaluation numérique de la précision globate du système[END_REF] [START_REF] Mainguy | Projet BIRAMIS-Mesure du bilan radiatif de l'atmosphère terrestre par satellite accélérométrique[END_REF]. Today, the instrument accuracy and satellite design capabilities have much improved, paving the way for a successful mission. This paper represents a first step towards a potential mission design for measuring the EEI directly from space. We revisit the measurement of radiation pressure and examine whether current measurement capability provides the accuracy and precision to estimate the global and regional mean EEI at TOA to at least within ±0.3 Wm -2 (see section IV). In section II we describe the spatial and temporal nature of EEI as we understand it from analysis of CERES EBAF data. Section III outlines the theoretical framework of the EEI derived from radiation pressure measurements. In sections IV and V, we present and quantify to the extent possible instrument requirements and impacts of perturbing forces. A brief summary of early results based on CACTUS measurements is provided to demonstrate the overall feasibility of this approach in section VI. Sections VII and VIII concern the instrument and potential spacecraft characteristics. We briefly discuss potential orbit and sampling considerations in section IX and conclude with a summary of remaining challenges in section X.

Index Terms-Low

II. TEMPORAL AND SPATIAL NATURE OF EEI

The concept presented here predominantly aims at the measurement of long-term global mean EEI, but we briefly discuss aspects of spatial and temporal variability to provide first-order accuracy and sampling requirements. Although beyond the scope of this paper, temporal and spatial sampling considerations are crucial for the best possible estimate of annual global mean EEI (see also section IX). Figure 1 shows a time series of monthly anomalies (gray) and the 12-month running mean (purple) of EEI between March 2000 to January 2017 based on CERES EBAF edition 4.0 (https://ceres-tool.larc.nasa.gov/ord-tool/jsp/EBAF4Selection. jsp). The anomalies reflect the internal variability of the climate system, predominantly that of ENSO, dipping significantly in response to the 2007 and 2009 El Niño events, and peaking in La Niña periods (2008,2012). The range of interannual variability is at 0.7 Wm -2 (1σ) and of the same order as the longterm mean of EEI (0.7±0.1 Wm -2 ) to which the data product has been adjusted [START_REF] Johnson | Improving estimates of Earth's energy imbalance[END_REF]. A significant trend at 0.4 Wm -2 per decade is observed over 2001-2015. To detect a trend of that order with 20% uncertainty would take about 18 years using a perfect observing system with no measurement uncertainty. Adding a measurement uncertainty at 0.3 Wm -2 (see section IV) increases the detection time beyond 38 years. These detection times were estimated using EEI monthly anomalies and the trend time detection formulae after [START_REF] Leroy | Climate Signal Detection Times and Constraints on Climate Benchmark Accuracy Requirements[END_REF]. From this we take, that trends in EEI may not be detectable within the scope of a typical mission lifetime of three to ten years, but the interannual (σ=0.7 Wm -2 ) and seasonal variability of global mean EEI (σ=7 Wm -2 ), as well as the zonal variability of multi-annual means (σ=64 Wm - 2 ) are detectable at a measurement accuracy better than 0.7 Wm - 2 . The black line in Figure 1 represents the timeseries of global mean ocean heat storage (OHS) calculated from the average ocean heat content of three Argo-based datasets as computed by [START_REF] Stephens | The Curious Nature of the Hemispheric Symmetry of the Earth's Water and Energy Balances[END_REF] in terms of running means of four seasonal anomalies. Although this averaging strongly reduces the amplitude and noise in the seasonal anomalies (σ >2 Wm -2 ), the interannual variability substantially disagrees with the EEI estimates from CERES EBAF, presumably a result of sampling errors (see Section I). Figure 2a is a global map of the multi-annual mean EEI (2000-2017). On average, the EEI is positive in the tropics and negative over the poles with near zero values at the mid latitudes. Being the sum of incoming solar radiation, reflected solar radiation, and Earth's thermal emission, we expect a positive net radiative flux to induce a net "inward" acceleration on the spacecraft when at lower latitudes, and a net "outward" acceleration at higher latitudes. Figure 2b shows the climatological mean standard deviation within each zonal band per month. The largest spatial variability in EEI is found between 10° to 30° North throughout the year and related to the variable surface reflectivity of the oceans and bright desert areas encompassed by these zones. High values are also seen at higher latitudes on both hemispheres during respective summer seasons, a result of variable insolation and surface properties of the polar regions (ice-free ocean versus ice/snow covered ocean and land). This gives some idea on where frequent observations are preferable to cover the spatial variability of climatological mean EEI. Figure 2c shows the annual mean (2016) diurnal cycle of EEI averaged over the tropical band (30°S-30°N) derived from CERES SYN1deg data (https://ceres.larc.nasa.gov/products.php?product=SYN1deg). This dataset uses information from geostationary satellites to incorporate diurnal variability and reduce spatial sampling errors [START_REF] Doelling | Geostationary enhanced temporal interpolation for CERES flux products[END_REF]. In this zonal band, the EEI varies in concert with longwave and shortwave outgoing fluxes, which peak around noon and 9 am (UTC), respectively. The shading indicates the seasonal scatter in terms of ±1𝜎. Naturally, the annual mean diurnal cycle of the tropics is smoothed out by the zonal and annual averaging, but is in essence what the concept proposed here should aim to capture. The estimates derived here represent first order requirements for detecting and sampling EEI spatial and temporal variability; the discussion of requirements for measurement accuracy will be refined in section IV. III.

THEORY

A. Radiation pressure force

The effect of radiation pressure on artificial satellites has been studied extensively since the onset of space exploration (e.g., [START_REF] Wyatt | The effect of terrestrial radiation pressure on satellite orbits[END_REF][44] [START_REF] Krivov | Orbital evolution of highaltitude balloon satellites[END_REF]). Here, we provide the theoretical basis that connects radiation pressure measurements to the EEI based in part on [START_REF] Vonder Haar | Theoretical Comparison Between Radiometric and Radiation Pressure Measurements for Determination of the Earth's Radiation Budget[END_REF]. From the Einstein mass-energy conservation principle follows the equivalence between photon energy and momentum. Therefore, when a photon impinges on an object and is either reflected or absorbed, its momentum is removed and conveyed to the object, resulting in a radiation pressure force that induces an acceleration of the object, i.e. spacecraft. This acceleration can be measured by an accelerometer of sufficient sensitivity situated in the center of the spacecraft. The radiation pressure vector force 𝑃 # ⃗ exerted on an object of mass m is a function of the spectral radiative flux 𝐹 ⃗ (𝜆), the Since the two-dimensional tensor 𝐶 *+, (𝜆, 𝜃) can change the direction of 𝑃 # ⃗ with respect to 𝐹 ⃗ (𝜆), the acceleration 𝑎 ⃗ is not necessarily co-linear with the direction of 𝐹 ⃗ (𝜆) unless the incident angle (𝜃) and spectral (𝜆) dependence are eliminated. This can be achieved by considering a spherical object (independent of 𝜃) whose surface's thermo-optical properties are independent of 𝜆. [46][47]. The co-linearity between 𝐹 ⃗ (𝜆) and 𝑎 ⃗ is a prerequisite for the derivation of EEI from radiation pressure force 𝑃 # ⃗ (see section B). Under the assumption of no spectral dependence and considering a spherical object with radius 𝑟, the effective crosssection can be defined as follows. The object coating's thermooptical properties are distinguished between the coating's absorptivity (A), total reflectivity R, specular reflectivity RS, diffuse reflectivity RD, transmissivity T (here = 0), and emissivity (𝜀), 𝑤hereby 𝐴 + 𝑅 = 1, 𝑅 Q + 𝑅 R = 𝑅, 𝜀 ≤ 𝐴.

According to [START_REF] Vonder Haar | Theoretical Comparison Between Radiometric and Radiation Pressure Measurements for Determination of the Earth's Radiation Budget[END_REF] it follows for the absorption cross-section: 𝜎 U = 𝐴 𝜋𝑟 W , the specular cross-section: 𝜎 X Y = 𝑅 Q 𝜋𝑟 W , the diffuse reflective cross-section: 𝜎 X Z = 𝑅 R [ \ 𝜋𝑟 W , and the diffuse emission cross-section: 𝜎 ] = 𝜀 2 \ 𝜋𝑟 W , which represents a parasitic term. The total effective cross-section of an absorbing-reflecting spherical object is then:

𝐶 *+, = 𝜎 = 𝜋𝑟 W (𝐴 + 𝑅 Q + 𝑅 R + X Z \ ) (3)
= 𝜋𝑟 W (1 + 𝑅 R 3 ) = Σ * 𝐾
where Σ is the actual geometric cross-section 𝜋𝑟 W and K is the coating property coefficient, under the assumption of no spectral dependence. K equals 1 if the object is either perfectly absorbing or specular reflecting.

Considering the net radiative flux as the sum of the solar, lunar and terrestrial sources, there will be non-zero acceleration of the spherical object along the x, y, and z components in threedimensional space. The sum of these acceleration components yields the effective net radiation pressure induced acceleration 𝑎 ⃗ b*, co-linear with the direction of incident net radiative flux 𝐹 ⃗ . In a rotated coordinate system where the z vector component of 𝑎 ⃗ b*, is along the radial axis from the Earth's center, a spherical spacecraft will undergo an acceleration in the radial direction

𝑎 ⃗ c = 𝐹 ⃗ c * d * e f * g (4)
where 𝐹 ⃗ c is the net radiative flux along the radial direction normal to a horizontal surface at the spacecraft location [START_REF] Vonder Haar | Theoretical Comparison Between Radiometric and Radiation Pressure Measurements for Determination of the Earth's Radiation Budget[END_REF]. Needless to say, this only holds in an environment in which other non-gravitational forces are either held constant or are negligibly small (see section V).

B. From acceleration to flux

The global mean EEI at the TOA represents the net radiative flux through a sphere around Earth, provided the observing system's orbit is circular. The surface flux through this sphere is independent of the direction of the net radiative flux, only the radial component of the net radiative flux contributes to the sphere's surface flux. More specifically, EEI is the surface integral of the net radiative flux component normal to the horizontal surface at the TOA, where the net radiative flux is the sum of incoming solar radiation, reflected solar radiation, and the Earth's emitted thermal radiation. The geometry of the relation between the net radiative flux on a horizontal surface (TOA) and the radial acceleration that it induces is highlighted in Figure 3. The net radiative flux through some horizontal surface element dS at the TOA is 𝐹 • 𝑛 (schematically represented by the green arrows), where n is the surface normal and F is the constant net radiative flux vector field (yellow arrows). This means, the net 'surface' flux through the TOA (location of spacecraft) can be derived from 𝐹 • 𝑛 solely, and knowledge of the direction of 𝐹 is redundant. If F induces an acceleration anet (black arrows) that is co-linear to its direction, 𝐹 • 𝑛 (or Fr, see previous section) is associated with an acceleration along the radial direction aR (orange arrows), the radial component of anet. Therefore, to facilitate EEI observations via accurate measurements of aR, the induced accelerations anet have to be co-linear to the impinging net irradiances. This only holds, if we assume a spacecraft of spherical shape, which also avoids polarization effects [START_REF] Duchossois | Potential European climatological satellite missions: SEOCS and BIRAMIS[END_REF], and with constant near-perfect absorbing or reflecting coating properties (K=1) that are independent of wavelength and incident angle. Different coating materials that yield property coefficients (K) near 1 have been assessed in the wake of BIRAMIS related studies [START_REF] Duchossois | Potential European climatological satellite missions: SEOCS and BIRAMIS[END_REF], and are briefly summarized in section VIII.

The definition of the net 'surface' flux through TOA and its relation to measurable radial accelerations induced by 𝐹 • 𝑛, facilitate the direct measurement of EEI, and help to eliminate the perturbing effect of atmospheric drag (see section V.) While this theoretical framework is appealing, the measurement of radiation flux via radiation pressure is an intricate multi-part problem and requires high instrument sensitivity and optimal spacecraft design as a first prerequisite. The accelerometer MicroSTAR developed at ONERA, France, fulfills the requirements of accuracy and stability and is presented in section VII together with planned calibration procedures. Second, the vector field F is not constant and varies with time and location, as does its normal component 𝐹 • 𝑛. Therefore, further study is needed to determine the measurement accuracy of the radial acceleration as a function of time and position, and in dependence of different illumination angles, synoptic weather patterns, and spacecraft characteristics. Third, the removal of parasitic forces or confounding variables, respectively, is crucial to isolate the accelerations due to radiation pressure. This can be done by either minimizing their impact by certain geometric and orbital design considerations or by modeling. Some of the leading confounding variables and their average magnitude are presented in section V. Fourth, from the perspective of mission design, spatio-temporal sampling considerations will shape the orbital configuration in which one or multiple spacecrafts are foreseen to provide global mean estimates of EEI within acceptable error bounds derived in Section IV. The quest for such an optimal configuration is subject of future research and briefly discussed in Section IX. Fifth, to obtain a climate data record instrumental in radiation budget studies, temporal and spatial interpolation schemes and flux deconvolution to an optimal TOA level (~20km [START_REF] Loeb | Defining Top-of-the-Atmosphere Flux Reference Level for Earth Radiation Budget Studies[END_REF]) are essential and subject of future study. These design and processing steps will eventually provide the basis for a higherlevel product of global and zonal mean EEI on monthly and annual time scales.

For the remainder of the paper, when we derive requirements (section IV) and the average magnitude of confounding effects (section V), we refer to a spherical satellite with K=1, mass=50kg and r=0.5m. The orbit height we set to 1300 km, an altitude well below the Van Allen belts at which the impact of aerodynamic drag is minimized, and potentially a "sweet spot" for the spatio-temporal sampling via multiple spacecrafts (section IX).

IV.

REQUIREMENTS

Accuracy requirements for the radiative flux components of the energy balance have been established by the community [START_REF] Ohring | Achieving satellite instrument calibration for climate change (ASIC)[END_REF][51] and WMO's Global climate observing system [START_REF]The Global observing System for climate: Implementation[END_REF]. It follows that observing systems are required to measure incoming solar radiation (ISR) within ±0.01% (~0.034Wm -2 ) of the global annual mean (~340 Wm -2 ), the reflected solar flux (RSR) within ±0.3% (~0.3 Wm -2 , global annual mean at ~100 Wm -2 ), and the Earth emitted thermal radiation (IR) at ±0.1% (~0.24Wm -2 , global annual mean at ~240 Wm -2 ), in order to enable meaningful interpretation. None of these sources define directly an uncertainty requirement for the EEI, but an error expansion yields ±0.386Wm -2 . This is equivalent to conducting a 0.1% measurement with respect to the global average ISR.

[1] provide a more stringent absolute accuracy requirement at < 0.1 Wm -2 on account of the small absolute magnitude of EEI and its long-term variability of the order of tenths of Wm -2 .

Studies deriving EEI from ocean heat content changes (plus small contributions from changes in ice, land, and the atmosphere) report uncertainties in the range of ±0.1 to ± 0. instrument accuracy of the order of 10 -11 or even 10 -12 ms -2 is necessary to meet the requirements for Earth radiation budget studies. Figure 4 shows the net inward radial acceleration as simulated at different orbital positions in an idealized setup (aqua planet) for a perfectly absorbing spacecraft in a polar orbit crossing the equator at local noon. While the global mean EEI requires an acceleration sensitivity at about 10 -11 ms -2 , the acceleration due to local changes in EEI ranges between -4 to 5•10 -8 . Therefore, the steps to be taken to aggregate the measurements in time and space to an annual global mean estimate of EEI will be just as essential as the measurement accuracy itself in keeping the uncertainty small.

V.

CONFOUNDING VARIABLES

A number of confounding variables introduce uncertainty in the relation between EEI and the measured acceleration from radiation pressure (e.g., [46][48]). A list of such potentially perturbing forces and their estimated average magnitude is provided in Table 2 based on the assumption of a spherical spacecraft (r=0.5 m, m=50 kg) in a circular orbit at 1300 km altitude. CACTUS studies (e.g., [START_REF] Boudon | Synthesis of flight results of the Cactus accelerometer for accelerations below 10 -9 g[END_REF]) found most of the perturbing forces to be negligibly small with respect to the measurement accuracy achieved by the accelerometer at that time (~10 -10 ms -2 ). In light of a new generation of instruments and their higher sensitivity (10 -11 -10 -12 ms -2 ), the role of confounding variables is revisited here.

In the present paper, we focus on the three largest perturbing forces: the residual atmospheric drag, gravity, and the Yarkovsky effect. The magnitude of the average acceleration due to atmospheric drag is at 10 -9 ms -2 (Table 2) ten times larger than the variations due to radiation pressure (10 -8 ± 10 -11 ms -2 ). However, for a circular orbit and a spherical satellite, the drag force is directed along the satellite's velocity vector or travel direction [START_REF] Gaposchkin | Analysis of Satellite Drag[END_REF], respectively, hence acts orthogonal to the radial acceleration component. The associated lift effect at 1300 km is negligible [START_REF] Cook | The effect of Aerodynamic Lift on Satellite Orbits[END_REF][56] on spherical or near-spherical space crafts [START_REF] Ching | Effects of atmospheric winds and aerodynamic lift on the inclination of the orbit of the S3-1 satellite[END_REF] and might not affect the direct measurement of EEI via the radial acceleration component either. Nevertheless, [58][59] have noted that slight departures from perfect sphericity induce significant changes in drag effects. The study of capabilities to design the spacecraft as spherical as possible and the effect of departure is therefore crucial. To achieve an EEI measurement within ± 0.1% of ISR, strict requirements must follow for the circularity of the orbit (<0.3%), the sphericity of the spacecraft (<0.1%), and knowledge of its orientation (±22 arc min, <0.1%). Gravitational variations are another form of parasitic force acting on the spacecraft with a magnitude of approximately 10 - 5 ms -2 . However, these variations act in common mode on both the outer shell of the spacecraft and inner test mass of the accelerometer. Thus, the perturbing effect of gravitational variations on the direct measurement of radiation pressure is negligible.

Another disturbance follows from the acceleration due to thermal push induced by thermal gradients on the satellite skin and the anisotropy of its own thermal radiation. This effect is widely known as Yarkovsky effect and can be determined, knowing the temperature of the body following equation 5 after [START_REF] Alfonso | Orbital effects of LAGEOS seasons and eclipses[END_REF] and [START_REF] Mignard | Lageos: Ten years of quest for the non-gravitational forces[END_REF] who computed the thermal push of LAGEOS.

Here, we assume for a black sphere, due to sun and Earth irradiances, an equilibrium temperature 𝑇 k at 330K and a temperature gradient Δ𝑇 at 300K [START_REF] Poinas | Satellite Thermal Control Engineering (prepared for "SME 2004[END_REF].

𝐹 mn = 2o p ]q 3 𝜋𝑟 W 𝑇 k \ Δ𝑇 (5)
The associated acceleration is then at about 6•10 -8 ms -2 . Potential reduction of thermal gradients and associated emissivity variations could be achieved by spinning the satellite in orbit around its radial axis. For CACTUS, studies [START_REF] Boudon | Synthesis of flight results of the Cactus accelerometer for accelerations below 10 -9 g[END_REF] estimated thermal thrust at about 10 -10 ms -2 at a spin frequency of 10 -3 Hz, resulting in Δ𝑇 at 80K. The optimal spin frequency for the observing system presented here will depend on the satellite skin characteristics and accuracy requirements.

The other perturbing forces listed in Table 2 have been estimated for CACTUS at magnitudes smaller than 10 -10 ms -2 (e.g., [START_REF] Boudon | Synthesis of flight results of the Cactus accelerometer for accelerations below 10 -9 g[END_REF][62]). While this magnitude was considered small with respect to the achieved measurement accuracy at that time, it now becomes potentially disturbing at improved instrument accuracy. Hence, revisiting the role and reducing the impact of these perturbing forces will be essential for the measurement of EEI with present-day capabilities.

PREVIOUS FEASIBILITY STUDIES

A number of studies [38][53][63] demonstrated the feasibility to estimate TOA radiative fluxes with the ultra-sensitive CACTUS accelerometer that flew onboard CASTOR in 1975/76 as the first of its kind. One-year worth of data was collected with sufficient accuracy to determine seasonal and latitudinal variations in ISR (at day-night transitions), IR (in shadow), and EEI (or net radiative flux) between 30°S and 30°N. The derived IR flux varied considerably between clear and overcast periods, as well as over land and ocean, hence allowed to get a sense of cloud effects and land-sea contrasts typical for IR variations. Overall, the derived radiation fluxes qualitatively agreed well with data from satellite radiometry [START_REF] Stephens | Earth radiation budgets[END_REF]. Figure 5 depicts the zonal variations in annual mean EEI derived from radial accelerations (acc., CACTUS) and modern radiometric data (CERES EBAF edition 4.0, 2000-2017). The accelerometric estimates exhibit a systematic offset with respect to the CERES data at almost 20 Wm -2 . The dashed lines represent measures of internal spatial and temporal variability in terms of standard deviation (σ) of monthly anomalies. σS represents the spatial scatter of monthly 1°x1° anomalies per latitude zone (equation 7 in [START_REF] Kato | Interannual variability of the global radiation budget[END_REF]), while σT represents the temporal scatter of zonally averaged monthly anomalies (equation 8 in [START_REF] Kato | Interannual variability of the global radiation budget[END_REF]). The accelerometric estimates are well outside the σT and σS lines, meaning the large difference cannot be explained by natural variability. The reason for this discrepancy is not fully known, but was partly attributed to wrongly assigned radiation pressure coefficients needed to translate the measured radial accelerations into radiative flux [START_REF] Boudon | Synthesis of flight results of the Cactus accelerometer for accelerations below 10 -9 g[END_REF]. Nevertheless, given the high sensitivity to spatial and seasonal variations in radiative flux, an observation system optimally designed for the measurement of EEI, in which biases are known and can be eliminated, will allow to improve absolute accuracy. The almost spherical (radius: 0.8m, mass: 76kg) CASTOR was originally developed to measure air-density and detect micrometeoroids in low atmospheric density (apogee: 1270km, perigee: 270km, inclination: 30°). The achieved measurement sensitivity exceeded expectations and was further augmented using statistical methods [START_REF] Boudon | Measurement of the radiation pressure by accelerometry: A new way to the determination of the Earth radiation budget. Result obtained with CASTOR/CACTUS experiment[END_REF] reaching 10 -10 ms -2 (or about 1 Wm -2 ), which ultimately allowed the first evaluation of EEI from space. Overall, the CACTUS studies concluded that accelerometry provides viable means to observe the EEI, but recommended to consider a different choice for satellite skin material, orbit definition, and good knowledge of attitude parameters. ESA's BIRAMIS project studies [START_REF] Duchossois | Potential European climatological satellite missions: SEOCS and BIRAMIS[END_REF] did consider a more suitable concept design that improved the accuracy of the measurement as it relates to EEI. The uncertainty was at about 3 Wm -2 (only accelerometer measurement error) still an order of magnitude above present-day requirements (~0.3 Wm - 2 ). Data from high precision accelerometers flown on missions such as GRACE [START_REF] Tapley | The Gravity Recovery and Climate Experiment: Mission Overview and Early Results[END_REF], or GOCE [START_REF] Allasio | GOCE: space technology for the reference earth gravity field determination[END_REF] are potentially useful to study the impact of radiation pressure on Earth orbiting satellites over the past decade, although these missions are not optimized for such measurement. The satellites' non-uniform shape, inadequate characterization of thermo-optical properties and thermal control, as well as their relatively low orbits confound the measurement. While these data will not provide an estimate of EEI at high accuracy, they might allow to reproduce the amplitude of radiation variability to some degree, and provide insights into the change of satellite skin properties over time (see also Section VIII).

VII.

INSTRUMENT DESIGN: MICROSTAR

Since the employment of CACTUS in 1975, the French Aerospace Lab ONERA has built new accelerometers based on the same principle, but with improved performance that were launched in missions like CHAMP (2000) [START_REF] Reigber | The CHAMP geopotential mission[END_REF], GRACE (2002) [START_REF] Tapley | The Gravity Recovery and Climate Experiment: Mission Overview and Early Results[END_REF], GOCE (2007) [START_REF] Allasio | GOCE: space technology for the reference earth gravity field determination[END_REF] and GRACE-FO (scheduled in 2018) [START_REF] Flechtner | Status of the GRACE Follow-on mission[END_REF]. For the measurement of EEI, a sensitivity of at least 10 -11 ms -2 is required, at least for the accelerations along the radial axis. To further provide good attitude control of the satellite, an accelerometer providing angular acceleration is a great advantage. Here, we propose to use the accelerometer MicroSTAR, that was built based on similar principles as the previous generation, with a cubic proof-mass, but with three very sensitive axes instead of only two, providing angular accelerations at high accuracy [START_REF] Christophe | A new generation of ultra-sensitive electrostatic accelerometers for GRACE Follow-on and towards the next generation gravity missions[END_REF]. The instrument's measurement accuracy is required to be <0.1%, which implies a specification of the scale factor of the instrument.

A. Description

The principle of electrostatic accelerometers is to control a free proof-mass to be motionless inside an electrode cage. The force applied to maintain the proof-mass at the center of the electrode cage is proportional to the relative acceleration between the proof-mass and the electrode cage, which is fixed in the satellite. If the accelerometer is at the center of mass of the satellite, the proof-mass experiences the same gravity acceleration as the satellite, but the satellite is exposed to the > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < surfaces forces, such as atmospheric drag and radiation pressure. Consequently, the accelerometer measures only the non-gravitational accelerations.

In case of ONERA's electrostatic accelerometers, the proofmass motion is precisely measured through capacitive detection between proof-mass and the electrodes [START_REF] Josselin | Capacitive detection scheme for space accelerometers applications[END_REF]. A controller applies voltages to the same electrodes in order to create electrostatic forces, which counteract the relative acceleration between proof-mass and the electrode cages due to nongravitational forces. The measurement of the accelerometer is therefore the voltages applied to the electrodes [START_REF] Touboul | Electrostatic space accelerometers for present and future missions[END_REF].

The electrode cage of MicroSTAR is composed of six Ultra Low Expansion material (ULE) electrode plates with two electrodes that surround a cubic 30x30x30mm proof-mass (Figure 6). The electrode plates are manufactured with patented 3-Dimensional Ultra Sonic machining to draw the electrodes.

The electrode surfaces are covered with a conductive metallic coating manufactured using a Physical Vapor Deposition (PVD) process. The mechanical core of the accelerometer is fixed on a sole plate and enclosed in a hermetic housing in order to maintain cleanliness and vacuum around the proof-mass. The proof-mass is polarized with a very thin wire. The two pairs of electrodes of each axis control two degrees of freedom, one translation and one rotation of the proof-mass.

The accelerometer electronic architecture is composed of six control loops, one for each degree of freedom of the proof-mass. Along each of the three axes, one translation and one rotation are controlled by similar schemes. The electronic boards with the capacitive detector, controller and drive voltage amplifier take advantage of the previous accelerometers design with low noise and low consumption analog functions. The total weight of the accelerometer is estimated at 9.5 kg, with a power consumption of 10W.

B. Performance

In reality, due to the non-perfect location of the accelerometer at the center of mass of the satellite, the acceleration at accelerometer location 𝑎 U33 is perturbed by the gravity gradient 1 Underlined letters refer to a vector, while a letter between square brackets refers to a matrix.

([U]), the attitude control ([Ω] and uΩ ̇w) 1 , and by the motion of the accelerometer location 𝑟 U33 with respect to the center of mass 𝑟 5xy , according to [START_REF] Balmaseda | The Ocean Reanalyses Intercomparison Project (ORA-IP)[END_REF]:

𝑎 U33 = 𝑎 z{ + |-[𝑈] + uΩ ̇w + uΩ W w•|𝑟 U33 -𝑟 5xy • + 2[Ω]|𝑟̇U 33 -𝑟̇5 xy • + |𝑟̈U 33 -𝑟̈5 xy • (6)
To minimize the perturbation, it is important to localize the accelerometer at the center of mass of the satellite. Moreover, it is important to avoid any motion inside the satellite, such as liquid propellant. Furthermore, the measurement suffers of scale factor error [K], alignment error [R], coupling error [S], quadratic factor [K2], bias b and noise n:

𝑎 y*'ƒ = ([𝐼] + [𝐾] + [𝑆] + [𝑅])𝑎 U33 + [𝐾2]𝑎 U33 W + 𝑏 + 𝑛 (7)
For this mission, the proof-mass is made of Arcap alloy, with a weight of 218 g. The gap between electrodes and the proofmass is chosen at 400 µm in order to achieve the requirement. The accelerometer range is at 3.5•10 -6 ms -2 larger than the maximum acceleration level given in Table 2 (we recall that the gravity acceleration is not seen in the measurement).

The measurement suffers from an important bias due to the stiffness of the thin wire which polarizes the proof-mass (and avoids charging in orbit). The level is evaluated to less than 1.8•10 -6 ms -2 and shall be calibrated or rejected in orbit (see section VII C).

Figure 7 provides the spectral density of the noise and its main contributors according to the mathematical model of the accelerometer noise confirmed by previous missions [START_REF] Bergé | GOCE accelerometers data revisited: stability and detector noise[END_REF].

Considering a spin frequency at 10 -3 Hz, the accuracy of the measurement corresponds to the noise at this frequency (10 -11 ms -2 /Hz 1/2 ) multiplied by the square root of the frequency, which gives an accuracy of 3•10 -13 ms -2 rms. This translates into 0.01 Wm -2 using equation 4.

The other contributors of error will be minimized to have a negligible impact. For example, to avoid the projection of atmospheric drag along the track of the radial measurement, the alignment and coupling of the accelerometer shall be better than 100 µrad, which was realized in the GOCE mission.

C. Calibration

The electrostatic accelerometer suffers of an important bias, which shall be calibrated in order to be suppressed and to have long-term stability of the measurement. If the accelerometer is regularly turned by 180° with respect to the external acceleration, the signal in the measurement will change sign, but not the bias, allowing to correct for it. One can also consider a continuous spin of the instrument in order to modulate the external acceleration at spin frequency.

To do that, we propose to profit from the satellite spin used to equalize the satellite temperature and the thermo-optical properties along the irradiance direction. It is also possible to add a bias rejection system, which consists in general of a rotating platform inside the satellite [74] [75]. A combination of these methods can be used to calibrate along all three axes: Calibration along the radial axis could be achieved by spinning add a bias rejection system, which consists in general of a rotating platform inside the satellite [74] [75]. A combination of these methods can be used to calibrate along all three axes: Calibration along the radial axis could be achieved by spinning around the along-or cross-track axis, but this would hamper the communication to Earth or GPS. Adding a bias rejection system (rotating platform) to reject the bias along the radial axis together with a spin around the radial axis (at different frequencies) provides the means to reject the bias along all three directions. The accelerometer scale factor will be estimated on ground from the accurate measurement of its contributing sources, in particular the electrode surface and gap. These two main contributions do not vary in orbit, except through the temperature effect, which shall be accurately measured on board. An in-flight calibration of the scale factor is possible in orbit through the comparison of GPS position, knowledge of Earth's gravity field, and the accelerometer measurement along one orbit, but the accuracy of such calibration is to be assessed.

VIII.

SPACECRAFT DESIGN AND PAYLOAD

Important requirements of the prospective satellite system besides size, mass, and power consumption, concern the spacecraft's shape and coating characteristics. The satellite is not only the carrier of instrumentation but part of the measurement system itself, transforming the impinging irradiances into measurable accelerations. The employment of near-spherical spacecrafts is state-of-theart in improving atmospheric density models essential for precision orbit determination [54][76]. The LAGEOS missions and their observed orbital decay [START_REF] Barlier | Nongravitational perturbations on the semimajor axis of LAGEOS[END_REF] identified particle drag and radiation dependent forces as significant perturbations to a satellite's position in orbit. Likewise, a more recent mission, the Drag and Atmospheric Neutral Density Explorer (DANDE, [78][79]), aims at improving the understanding of the satellite drag environment in the lower thermosphere, but lost contact to ground systems shortly after launch. Since attitude motions neither change the cross-sectional area nor the area-to-mass ratio of a spherical spacecraft, the measurement of non-gravitational forces is simplified, which helps to reduce uncertainties in the quantification of drag coefficients [START_REF] Bowman | Drag Coefficient Variability at 175-500 km from the Orbit Decay Analyses of Spheres[END_REF] and radiation pressure [START_REF] Boudon | Synthesis of flight results of the Cactus accelerometer for accelerations below 10 -9 g[END_REF].

As outlined in section III, the spherical shape of the spacecraft is a crucial requirement for the successful monitoring of EEI via the measurement of radial accelerations and will reduce the perturbing impact of atmospheric drag. The design of a perfectly spherical spacecraft is likely impossible. An assessment of different near-spherical shapes that yield the required measurement accuracy is needed to provide design requirements.

To study satellite shape and skin material implications for BIRAMIS, ONERA and Aeritalia conducted payload and satellite definition studies with assistance by ESA [START_REF] Duchossois | Potential European climatological satellite missions: SEOCS and BIRAMIS[END_REF]. To find a material with constant coating property coefficient K close to 1, ONERA measured different skin material's optical properties at various wavelengths and angles of incidence. The two most stable choices were mechanically polished aluminum coated with MgF2 (specular reflecting) or black painted honeycomb (absorbing), as they induced the smallest measurement errors according to their numerical model [START_REF] Duchossois | Potential European climatological satellite missions: SEOCS and BIRAMIS[END_REF]. The studies found that variations in spectral absorption coefficient by 10% yield 1% variations in K, concluding that variations of optical properties with wavelength or ageing did not significantly modify K and therefore the measurement itself. Targeting EEI measurements to within at least ±0.3 Wm -2 , knowledge of K has to be better than ±0.1%; acceptable variability in K and the effect of degradation due to long duration exposure require reassessment with respect to the target accuracies proposed here. Liquid fuel disturbs the accelerometric measurement, hence solar cells and batteries are required to provide the needed power (estimated at 90W for BIRAMIS) during sunlight and eclipse. Ultimately, the number of solar cells needed depends on size, mass, surface area and power consumption of the spacecraft. A relatively large surface area of about 30% was estimated to be covered by solar cells in case of BIRAMIS (r=1meter, mass=225kg), distributed in a uniform patchwork pattern.

The accelerometer and a rotating platform for inflight calibration represent the primary payload of the spacecraft. Solar sensor and star trackers essential for attitude determination, as well as a GPS receiver and patch antenna for data transmission, ideally will not hamper significantly with the spherical shape and thermo-optical properties of the spacecraft. Given the different surfaces and non-uniform exposure to solar UV radiation that causes degradation, it is clear that the spacecraft will neither be perfectly absorbing nor spatially uniform. The radial spin and near-spherical shape of the satellite will help equalize varying non-isotropic thermo-optical properties, but the sun facing side may undergo more substantial degradation due to UV exposure and induce gradients in surface absorptivity. K, its change in time as function of wavelength, as well as the errors induced, will have to be estimated for all materials. Future assessment of coating types should also consider the minimization of thermal > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < gradients that induce thermal thrust and thermo-structural deformations that lead to perturbing inertial accelerations. Besides shape and satellite skin, we may think about maximizing the cross-section over mass ratio, which would enhance the acceleration measurement according to equation [START_REF] Trenberth | Insights into Earth's Energy Imbalance from Multiple Sources[END_REF]. Balloon-shaped satellites, such as the passive communication experiments Echo [START_REF] Jones | Solar Radiation Pressure Effects, Gas Leakage Rates, and Air Densities Inferred From the Orbit Of Echo I[END_REF] or PAGEOS represent a possible scenario. However, the viability of such a construction carrying an active instrument is questionable, since the risk of thermo-structural deformations, as occurred with ECHO I, has to be considered.

IX.

ORBIT & SAMPLING

The orbit choice is dictated by the need to minimize perturbing forces, such as atmospheric drag, the effects of energetic particles (Van Allen belts), and the need for global sampling. A compromise between those needs requires a near-circular orbit higher than 1000 km ( [START_REF] Harrison | Mission analysis to define satellite orbits for Earth radiation budget measurements[END_REF][48] [START_REF] Vonder Haar | Theoretical Comparison Between Radiometric and Radiation Pressure Measurements for Determination of the Earth's Radiation Budget[END_REF]) with an inclination of 90°.

To satisfy first-order spatio-temporal coverage requirements of measuring the radiation fluxes at six different longitudes and six latitudes at four times a day, the best configuration is met with three orbital planes, one of which is polar (90°) and the others slightly inclined. Each orbit is to be equipped with a spacecraft at 1300 km, an orbit altitude that represents a "sweet spot" of view factor (0.08) and period (112 minutes). These findings are in line with [START_REF] Harrison | Mission analysis to define satellite orbits for Earth radiation budget measurements[END_REF], who describe two and three satellite combinations to be most adequate in providing monthly global mean albedo and thermal radiation estimates based on WFOV sensors (non-scanning) within 1% (~2 Wm -2 ) to a simulated global mean reference. This sampling error is still large and attributable to the difficulty of measuring and modeling the diurnal cycle sufficiently [START_REF] Salby | Asynoptic Sampling Considerations for Wide-Field-of-View measurements of outgoing radiation. Part II: Dirunal and Random space-time variability[END_REF]. Even in case of the scanning CERES radiometers, where models can be used to augment the temporal sampling, a substantial error due to incomplete diurnal sampling has been identified: By adding more complete diurnal cycle information from geostationary satellites, the EEI derived from CERES is reduced by about 1 Wm -2 [START_REF] Doelling | Geostationary enhanced temporal interpolation for CERES flux products[END_REF]. The impact of incomplete diurnal sampling of RSR and IR on regional trends and interannual variability is, however, insignificant [START_REF] Taylor | Impact of Sun-Synchronous diurnal sampling on tropical TOA flux interannual variability and trends[END_REF].

Meeting the accuracy goal of ±0.3 Wm -2 or better, will require in-depth analysis and simulation of radiation pressure acceleration for different numbers of satellites and orbits using hourly radiation data. Such data can be obtained from CERES (https://ceres.larc.nasa.gov/products.php?product=SYN1deg) or from global climate model simulation. This future study will show whether more satellites are needed to resolve the mean diurnal cycle of EEI adequately and if interpolation techniques can help reduce sampling errors. A study by [START_REF] Gristey | Determination of global Earth outgoing radiation at high temporal resolution using a theoretical constellation of satellites[END_REF] found that a constellation of 36 satellites is needed to estimate global daily mean shortwave and longwave outgoing radiation to within 0.16 Wm -2 and -0.13 Wm -2 . Given that we aim at longer-term estimates of annual or potentially monthly resolution, a less dense coverage is likely sufficient. In addition to global annual and monthly mean EEI estimates, a data product of zonal resolution would meet GCOS requirements as aimed at by CLARREO [START_REF] Wielicki | CLARREO Pathfinder Mission: Enabling Faster Observation of Climate Change[END_REF], a radiometric mission that aims at providing TOA radiation balance components at high spectral resolution.

While we aim at high accuracy for global annual mean EEI to facilitate climate change detection studies, lower accuracy is sufficient to monitor seasonal and spatial variability (see section II).

X.

CHALLENGES & OUTLOOK

In this paper, we have outlined the complexity of estimating Earth's energy imbalance (EEI) directly from space. The measurement of the integrated value of EEI, as opposed to its radiative components, is a major challenge faced by the climate science community and requires rethinking our capabilities. While it is probable that radiometry may never provide the accuracy needed to pinpoint the true magnitude of EEI, the measurement of the individual radiative components is indispensable in understanding the causes of perturbations to the energy budget, addressing the question why the input of heat changes. Temporal ocean heat content changes represent to date the sole source of meaningful EEI estimates over the last decade, albeit sampling errors and the integration of additional sinks and sources of heat, such as ice melt that continuous to rise in a warming world [START_REF] Chen | Contribution of ice sheet and mountain glacier melt to recent sea level rise[END_REF], represent challenges. Vital information on the horizontal and vertical distribution of heat uptake are unique to the Argo observing system, irreplaceable by remote sensing techniques, and address the question on where the heat goes. Here, we propose to complement these existing observation systems by adding a third observation pillar that explicitly monitors how much heat is accumulated by our planet in the global mean, providing closure of the energy balance from space. A target accuracy for measurements of global mean EEI is not established by the community, but falls within ±0.1 to ±0.3 Wm -2 according to Argo-based capabilities [START_REF] Von Schuckmann | An imperative to monitor Earth's energy imbalance[END_REF] and GCOS recommendations for energy budget studies [START_REF]The Global observing System for climate: Implementation[END_REF]. Additional information on the zonal distribution of EEI would provide some information on where the heat goes and serve for regional energy budget studies and inter-comparisons between products.

Here, we revisited the methodology of deriving the net radiation flux at TOA from the net radiation pressure force acting on Earth orbiting spacecrafts. The feasibility has been demonstrated in the past by missions like CASTOR, which carried the CACTUS accelerometer [START_REF] Boudon | Measurement of the radiation pressure by accelerometry: A new way to the determination of the Earth radiation budget. Result obtained with CASTOR/CACTUS experiment[END_REF], and proposed concept studies leading to an unfulfilled mission, BIRAMIS [START_REF] Duchossois | Potential European climatological satellite missions: SEOCS and BIRAMIS[END_REF]. Since then, the measurement accuracy of the ultra-sensitive accelerometers employed to measure non-gravitational forces has greatly improved and a measurement of net radiative flux to within ±0.3 Wm -2 or better is within reach, depending on spacecraft design and orbital considerations that shape the measurement sensitivity and accuracy in their own way. The spacecraft itself represents an integral part of the measurement system as it converts the impinging irradiances into measurable accelerations. Requirements concerning the spacecraft's shape and optimal skin coating characteristics will continue to be subject of research.

Perturbing forces, such as atmospheric drag and the Yarkovsky effect, need to be thoroughly identified, their impact quantified, and eventual solutions presented. The two above mentioned effects become negligible when we consider a spinning, spherical spacecraft at an orbit altitude greater than 1000 km. > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < These requirements and related uncertainties need to be modeled and quantified within the trade space of estimating the EEI most accurately to within at least ±0.3 Wm -2 . This trade space may yield different solutions that depend on the ultimate goal of either aiming at the most accurate local estimate or the best-possible global mean. Considering the latter, spatial and temporal averaging will likely smooth out the noise and uncertainty induced by perturbing effects and design flaws of an imperfect observing system. Similarly, the methodology of spatial and temporal sampling, by employing one or multiple spacecrafts and their added value, requires further evaluation. Finally, the processing of the measured accelerations will require thorough conversion, deconvolution to an optimal TOA level, and averaging algorithms that will provide global and zonal mean EEI at annual and potentially monthly time scales that meet the requirements of the community. Table 3 summarizes the outstanding issues to address in order to establish a complete error budget of error sources, their contribution to measurement uncertainty, and solutions for their mitigation. The present paper has highlighted and in part quantified these issues and potential solutions. Showstoppers are so far not identified, paving the way to a better understanding of global climate change through an independent measurement of Earth's energy imbalance from space. Assessment of confounding variables and their error contribution with respect to established target accuracy. Establish solutions to reduce impact of perturbing forces.

5.

Spacecraft and mission design studies with focus on shape, thermo-optical properties, thermal control, degradation, and associated impacts on absorptivity and emissivity.

  Earth orbit satellites, Global warming, Remote sensing, Earth's energy imbalance, Accelerometer I.

Figure 1 :

 1 Figure 1: Global mean EEI (CERES EBAF edition 4.0) in terms of monthly anomalies (gray) and 12-months running means (purple) together with ±1σ ranges and Argo-based ocean heat storage (OHS) estimates in terms of four seasons running means of seasonal anomalies (black).

Figure 2 :

 2 Figure 2: a) Annual mean (2000-2017) net radiative flux at TOA (CERES EBAF) and b) the annual cycle of zonal standard deviation of net flux and c) tropical (30°S-30°N) annual mean (2016) diurnal cycle (CERES SYN1deg).

3 𝐶

 3 REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < speed of light c, and the effective extinction cross-section 𝐶 *+, that depends on the actual cross-section of the object, the thermo-optical properties of the object surface, the flux wavelength (𝜆) and the flux incident angle (𝜃). 𝑃 # ⃗ = 𝑚𝑎 ⃗ = 2 *+, (𝜆, 𝜃) 𝐹 ⃗ (𝜆) (1)For the acceleration vector (𝑎 ⃗) due to radiation pressure 𝑃 # ⃗ follows from[START_REF] Von Schuckmann | An imperative to monitor Earth's energy imbalance[END_REF]

Figure 3 :

 3 Figure 3: Schematic of measured net and radial accelerations (blue and orange arrows) induced by constant flux vector field (yellow).

F

  = constant flux vector field (e.g. net radiative flux) n = unit vector F•n dS n Earth's radius + h Satellite in circular orbit around Earth dS ! " # $ &' ' TOA a net co-linear with F decomposed in radial component a R and component in travel direction

  4 Wm -2 (e.g.,[START_REF] Von Schuckmann | An imperative to monitor Earth's energy imbalance[END_REF][13][START_REF] Schuckmann | How well can we derive Global Ocean Indicators from Argo data?[END_REF][START_REF] Trenberth | Earth's Energy Imbalance[END_REF]), again suggesting a target accuracy better than the ±0.4 Wm -2 derived above. The lack of an established target accuracy emphasizes the need for community-wide research on requirements. Following equation 4, we estimate the accelerations due to radiation pressure (aR) acting on a spherical, perfectly absorbing (K=1) spacecraft with mass of 50 kg and radius of 0.5 m for the different radiative flux components outlined above. The estimated accelerations, global mean fluxes and required accuracy are presented in Table1. The magnitude of accelerations due to the shortwave and longwave fluxes are on the order of 0.5 to 2•10 -8 ms -2 . Their uncertainty is between 0.02 to 1•10 -10 ms -2 , a similar magnitude as for the global mean value of EEI at about 3•10 -11 ms -2 . From this we deduce that an

Figure 4 .

 4 Figure 4. Net inward radial acceleration aR as function of orbital position, assuming a perfectly absorbing spherical spacecraft (m=50kg, r=0.5m) in a circular orbit (1300km) that crosses the equator at solar noon (solar equinox).

Figure 5 :

 5 Figure 5: Zonal averages of TOA net radiation flux (Wm -2 ) derived from CACTUS accelerations (1975-1976, orange) and CERES EBAF (2000-2017, gray) between 30°S -30°N. Bright blue dashed lines represent the spatial ±1σs of monthly 1°x1° anomalies per latitude (equation 7 in Kato, 2009), while the dark blue lines represent the temporal ±1σt of zonally averaged monthly anomalies (equation 8 in Kato, 2009).

Figure 6 .

 6 Figure 6. Mechanical core of the MicroSTAR accelerometer.

Figure 7 .

 7 Figure 7. Noise Performance of the MicroSTAR accelerometer with the main contributors: detector noise (red), thin wire damping (blue), measurement analog digital converter (green), contact potential difference (yellow), measurement analog noise (magenta), and bias fluctuation noise (brown).

TABLE 2

 2

		CONFOUNDING VARIABLES AT 1300KM
		MAGNITUDE
	CF	OVER ORBIT	derivation & treatment
		(MS -2 )
	atm. drag	~1.6•10 -9 ± 3•10 -9	½ ρ V 2 Cd 𝜋𝑟 W / m
			may not affect EEI measurement via
			radial component of acceleration
	gravity	~9•10 -5	estimated from GRACE
			common mode for shell and inner test
			mass of accelerometer
	Yarkovsky	6•10 -8 ms -2	equation 5 with T0=330K, DT=300K
	effect		spinning
	electrical	< 10 -10 ms -2 or 1.6	Cactus studies
	drag	Wm -2
	lunar	< 10 -10 ms -2	Cactus studies
	illumination
	Lorentz	< 10 -10 ms -2	Cactus studies
	force
	Poynting	< 10 -10 ms -2	Cactus studies
	Robertson
	solar wind	< 10 -10 ms -2	Cactus studies
	inertial	< 10 -10 ms -2	Cactus studies
	acceleration
	magnetic	< 10 -10 ms -2	Cactus studies
	field force

TABLE 3 OUTSTANDING

 3 NEXT STEPS 1. Define target accuracy, which is not established by community, but appears to converge to within ±0.1 to ±0.3 Wm -2 for longterm global mean EEI. 2. Simulation of radial accelerations as experienced by spacecraft due to Sun and Earth radiation, i.e. the net radiative flux or EEI, to assess accuracy of local measurement for different time and space resolutions, illumination angle, weather conditions, and space craft characteristics. 3. Study of diurnal cycle representation and associated sampling error for one, two, or three satellite systems. Identify optimum configuration for global mean sampling in annual and monthly mean and establish interpolation techniques to mitigate error. 4.

𝐹 *d * e f with F=radiative flux, Σ= actual cross-section 𝜋𝑟 W , r=0.5m, K=1 (perfectly absorbing), m=50kg, c=speed of light

Acknowledgment

The research was carried out at the Jet Propulsion Laboratory (JPL), California Institute of Technology, under a contract with the National Aeronautics and Space Administration. We would like to acknowledge the participants of the A-team study conducted at JPL who helped develop this research. This work was supported under NASA contract NNN12AA01C. Copyright 2018. All rights reserved.

XI.

This work was supported in part by the U.S. Department of Commerce under Grant BS123456."