Toward variational data assimilation for coupled models: first experiments on a di↵usion problem

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              "entity_revision:paragraph:appoggio_document_fr" => array:11 [ …11]
              "entity_revision:paragraph:appoggio_introductory_text" => array:11 [ …11]
              "entity_revision:paragraph:appoggio_last_refresh" => array:11 [ …11]
              "entity_revision:paragraph:appoggio_other" => array:11 [ …11]
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              "entity_revision:paragraph:appoggio_query_arguments" => array:11 [ …11]
              "entity_revision:paragraph:appoggio_session_row_type" => array:11 [ …11]
              "entity_revision:paragraph:appoggio_title" => array:11 [ …11]
              "entity_revision:paragraph:block_card" => array:11 [ …11]
              "entity_revision:paragraph:card" => array:11 [ …11]
              "entity_revision:paragraph:committee_session_row_files" => array:11 [ …11]
              "entity_revision:paragraph:dataset_parameters_bundle" => array:11 [ …11]
              "entity_revision:paragraph:multilanguage_video" => array:11 [ …11]
              "entity_revision:paragraph:new_row" => array:11 [ …11]
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              "entity_revision:paragraph:session_row" => array:11 [ …11]
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              "entity_revision:date_format" => array:12 [ …12]
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              "entity_revision:entity_form_mode" => array:12 [ …12]
              "entity_revision:entity_view_mode" => array:12 [ …12]
              "entity_revision:base_field_override" => array:12 [ …12]
              "entity_revision_reference" => array:8 [ …8]
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              "metatag" => array:8 [ …8]
              "search_api_text" => array:8 [ …8]
              "search_api_html" => array:8 [ …8]
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              "solr_multisite_document" => array:9 [ …9]
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              "email" => array:9 [ …9]
              "binary" => array:8 [ …8]
              "datetime_iso8601" => array:8 [ …8]
              "timestamp" => array:8 [ …8]
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              "any" => array:8 [ …8]
              "uri" => array:8 [ …8]
              "timespan" => array:8 [ …8]
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              "boolean" => array:8 [ …8]
              "map" => array:8 [ …8]
              "integer" => array:8 [ …8]
              "list" => array:8 [ …8]
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              "duration_iso8601" => array:8 [ …8]
              "entity" => array:10 [ …10]
              "entity:route_config" => array:12 [ …12]
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              "entity:bibcite_reference" => array:12 [ …12]
              "entity:bibcite_reference:artwork" => array:11 [ …11]
              "entity:bibcite_reference:audiovisual" => array:11 [ …11]
              "entity:bibcite_reference:bill" => array:11 [ …11]
              "entity:bibcite_reference:book" => array:11 [ …11]
              "entity:bibcite_reference:book_chapter" => array:11 [ …11]
              "entity:bibcite_reference:broadcast" => array:11 [ …11]
              "entity:bibcite_reference:case" => array:11 [ …11]
              "entity:bibcite_reference:chart" => array:11 [ …11]
              "entity:bibcite_reference:classical" => array:11 [ …11]
              "entity:bibcite_reference:conference_paper" => array:11 [ …11]
              "entity:bibcite_reference:conference_proceedings" => array:11 [ …11]
              "entity:bibcite_reference:corporate_document" => array:11 [ …11]
              "entity:bibcite_reference:database" => array:11 [ …11]
              "entity:bibcite_reference:education_material" => array:11 [ …11]
              "entity:bibcite_reference:film" => array:11 [ …11]
              "entity:bibcite_reference:government_report" => array:11 [ …11]
              "entity:bibcite_reference:hearing" => array:11 [ …11]
              "entity:bibcite_reference:journal" => array:11 [ …11]
              "entity:bibcite_reference:journal_article" => array:11 [ …11]
              "entity:bibcite_reference:legal_ruling" => array:11 [ …11]
              "entity:bibcite_reference:magazine_article" => array:11 [ …11]
              "entity:bibcite_reference:manuscript" => array:11 [ …11]
              "entity:bibcite_reference:map" => array:11 [ …11]
              "entity:bibcite_reference:miscellaneous" => array:11 [ …11]
              "entity:bibcite_reference:miscellaneous_section" => array:11 [ …11]
              "entity:bibcite_reference:newsletter" => array:11 [ …11]
              "entity:bibcite_reference:newsletter_featured_article" => array:11 [ …11]
              "entity:bibcite_reference:newspaper_article" => array:11 [ …11]
              "entity:bibcite_reference:patent" => array:11 [ …11]
              "entity:bibcite_reference:personal" => array:11 [ …11]
              "entity:bibcite_reference:poster" => array:11 [ …11]
              "entity:bibcite_reference:presentation" => array:11 [ …11]
              "entity:bibcite_reference:proceedings" => array:11 [ …11]
              "entity:bibcite_reference:report" => array:11 [ …11]
              "entity:bibcite_reference:software" => array:11 [ …11]
              "entity:bibcite_reference:statute" => array:11 [ …11]
              "entity:bibcite_reference:technical_memorandum" => array:11 [ …11]
              "entity:bibcite_reference:thesis" => array:11 [ …11]
              "entity:bibcite_reference:unpublished" => array:11 [ …11]
              "entity:bibcite_reference:user_manual" => array:11 [ …11]
              "entity:bibcite_reference:website" => array:11 [ …11]
              "entity:bibcite_reference:web_article" => array:11 [ …11]
              "entity:bibcite_reference:web_project_page" => array:11 [ …11]
              "entity:bibcite_reference:web_service" => array:11 [ …11]
              "entity:bibcite_keyword" => array:12 [ …12]
              "entity:bibcite_contributor_role" => array:12 [ …12]
              "entity:bibcite_contributor_category" => array:12 [ …12]
              "entity:bibcite_reference_type" => array:12 [ …12]
              "entity:bibcite_contributor" => array:12 [ …12]
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              "entity:block_content" => array:12 [ …12]
              "entity:block_content:basic" => array:11 [ …11]
              "entity:block_content:block_custom_news_science" => array:11 [ …11]
              "entity:block_content:column_content_text" => array:11 [ …11]
              "entity:block_content:content_block" => array:11 [ …11]
              "entity:block_content:hero_charts" => array:11 [ …11]
              "entity:block_content:hero_learning" => array:11 [ …11]
              "entity:block_content:simple_card" => array:11 [ …11]
              "entity:blb_layout" => array:12 [ …12]
              "entity:blb_layout_option" => array:12 [ …12]
              "entity:blb_breakpoint" => array:12 [ …12]
              "entity:captcha_point" => array:12 [ …12]
              "entity:comment_type" => array:12 [ …12]
              "entity:comment" => array:12 [ …12]
              "entity:comment:comment" => array:11 [ …11]
              "entity:contact_form" => array:12 [ …12]
              "entity:contact_message" => array:12 [ …12]
              "entity:contact_message:feedback" => array:11 [ …11]
              "entity:contact_message:personal" => array:11 [ …11]
              "entity:content_moderation_state" => array:12 [ …12]
              "entity:content_moderation_notification" => array:12 [ …12]
              "entity:daterange_compact_format" => array:12 [ …12]
              "entity:editor" => array:12 [ …12]
              "entity:entity_browser" => array:12 [ …12]
              "entity:facets_facet" => array:12 [ …12]
              "entity:facets_facet_source" => array:12 [ …12]
              "entity:facets_summary" => array:12 [ …12]
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              "entity:feeds_feed:basic_page_from_api" => array:11 [ …11]
              "entity:feeds_feed:basic_page_from_csv" => array:11 [ …11]
              "entity:feeds_feed:committee_session_by_api" => array:11 [ …11]
              "entity:feeds_feed:dataset_from_api" => array:11 [ …11]
              "entity:feeds_feed:ecmwf_training_video_youtube" => array:11 [ …11]
              "entity:feeds_feed:import_github_c3s_sketchbook_e" => array:11 [ …11]
              "entity:feeds_feed:import_github_copernicus_trainin" => array:11 [ …11]
              "entity:feeds_feed:indico" => array:11 [ …11]
              "entity:feeds_feed:moodle" => array:11 [ …11]
              "entity:feeds_feed:newletter_from_api" => array:11 [ …11]
              "entity:feeds_feed:news_from_api" => array:11 [ …11]
              "entity:feeds_feed:news_from_csv" => array:11 [ …11]
              "entity:feeds_feed:numerical_products_from_api" => array:11 [ …11]
              "entity:feeds_feed:project_from_api" => array:11 [ …11]
              "entity:feeds_feed:science_blog_feed" => array:11 [ …11]
              "entity:feeds_feed:special_project_from_api" => array:11 [ …11]
              "entity:feeds_feed:staff_page_from_api" => array:11 [ …11]
              "entity:feeds_feed:submission_application_for_membe" => array:11 [ …11]
              "entity:feeds_feed:users_from_api" => array:11 [ …11]
              "entity:feeds_feed:video_from_api" => array:11 [ …11]
              "entity:feeds_feed:webform_from_api" => array:11 [ …11]
              "entity:feeds_feed_type" => array:12 [ …12]
              "entity:feeds_subscription" => array:12 [ …12]
              "entity:field_config" => array:12 [ …12]
              "entity:field_storage_config" => array:12 [ …12]
              "entity:field_collection" => array:12 [ …12]
              "entity:field_collection_item" => array:12 [ …12]
              "entity:file" => array:12 [ …12]
              "entity:filter_format" => array:12 [ …12]
              "entity:image_style" => array:12 [ …12]
              "entity:imce_profile" => array:12 [ …12]
              "entity:jsonapi_resource_config" => array:12 [ …12]
              "entity:language_content_settings" => array:12 [ …12]
              "entity:configurable_language" => array:12 [ …12]
              "entity:linkit_profile" => array:12 [ …12]
              "entity:media_type" => array:12 [ …12]
              "entity:media" => array:12 [ …12]
              "entity:media:audio" => array:11 [ …11]
              "entity:media:commitee_session_row_document" => array:11 [ …11]
              "entity:media:document" => array:11 [ …11]
              "entity:media:image" => array:11 [ …11]
              "entity:media:remote_video" => array:11 [ …11]
              "entity:media:video" => array:11 [ …11]
              "entity:menu_link_content" => array:12 [ …12]
              "entity:menu_link_content:menu_link_content" => array:11 [ …11]
              "entity:metatag_defaults" => array:12 [ …12]
              "entity:migration_group" => array:12 [ …12]
              "entity:migration" => array:12 [ …12]
              "entity:node" => array:12 [ …12]
              "entity:node:aifs_blog" => array:11 [ …11]
              "entity:node:committee_session" => array:11 [ …11]
              "entity:node:dataset" => array:11 [ …11]
              "entity:node:faq" => array:11 [ …11]
              "entity:node:indico_event" => array:11 [ …11]
              "entity:node:landing_page" => array:11 [ …11]
              "entity:node:newsletter_article" => array:11 [ …11]
              "entity:node:news_item" => array:11 [ …11]
              "entity:node:numerical_product" => array:11 [ …11]
              "entity:node:page" => array:11 [ …11]
              "entity:node:research_project" => array:11 [ …11]
              "entity:node:science_blog" => array:11 [ …11]
              "entity:node:shorthand_stories" => array:11 [ …11]
              "entity:node:special_project" => array:11 [ …11]
              "entity:node:staff_page" => array:11 [ …11]
              "entity:node:status_page" => array:11 [ …11]
              "entity:node:training" => array:11 [ …11]
              "entity:node:video" => array:11 [ …11]
              "entity:node:webform" => array:11 [ …11]
              "entity:node_type" => array:12 [ …12]
              "entity:path_alias" => array:12 [ …12]
              "entity:pfdp_directory" => array:12 [ …12]
              "entity:behavior_settings" => array:12 [ …12]
              "entity:rdf_mapping" => array:12 [ …12]
              "entity:redirect" => array:12 [ …12]
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              "entity:responsive_image_style" => array:12 [ …12]
              "entity:rest_resource_config" => array:12 [ …12]
              "entity:search_page" => array:12 [ …12]
              "entity:search_api_server" => array:12 [ …12]
              "entity:search_api_task" => array:12 [ …12]
              "entity:search_api_index" => array:12 [ …12]
              "entity:search_api_autocomplete_search" => array:12 [ …12]
              "entity:solr_request_handler" => array:12 [ …12]
              "entity:solr_request_dispatcher" => array:12 [ …12]
              "entity:solr_field_type" => array:12 [ …12]
              "entity:solr_cache" => array:12 [ …12]
              "entity:search_api_sorts_field" => array:12 [ …12]
              "entity:shortcut_set" => array:12 [ …12]
              "entity:shortcut" => array:12 [ …12]
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              "entity:shortcut:default" => array:11 [ …11]
              "entity:simple_cron_job" => array:12 [ …12]
              "entity:simple_sitemap_type" => array:12 [ …12]
              "entity:simple_sitemap" => array:12 [ …12]
              "entity:simple_sitemap_engine" => array:12 [ …12]
              "entity:smart_date_format" => array:12 [ …12]
              "entity:smart_date_rule" => array:12 [ …12]
              "entity:smart_date_override" => array:12 [ …12]
              "entity:action" => array:12 [ …12]
              "entity:menu" => array:12 [ …12]
              "entity:taxonomy_vocabulary" => array:12 [ …12]
              "entity:taxonomy_term" => array:12 [ …12]
              "entity:taxonomy_term:audience" => array:11 [ …11]
              "entity:taxonomy_term:catalogue" => array:11 [ …11]
              "entity:taxonomy_term:chart_type_2" => array:11 [ …11]
              "entity:taxonomy_term:committee" => array:11 [ …11]
              "entity:taxonomy_term:committee_idiom" => array:11 [ …11]
              "entity:taxonomy_term:committee_session_row_type" => array:11 [ …11]
              "entity:taxonomy_term:dataset" => array:11 [ …11]
              "entity:taxonomy_term:dataset_keywords" => array:11 [ …11]
              "entity:taxonomy_term:dataset_licences" => array:11 [ …11]
              "entity:taxonomy_term:dataset_var_names" => array:11 [ …11]
              "entity:taxonomy_term:educational_resources" => array:11 [ …11]
              "entity:taxonomy_term:funders" => array:11 [ …11]
              "entity:taxonomy_term:level" => array:11 [ …11]
              "entity:taxonomy_term:meteorological_parameters" => array:11 [ …11]
              "entity:taxonomy_term:newsletter_issues" => array:11 [ …11]
              "entity:taxonomy_term:newsletter_sections" => array:11 [ …11]
              "entity:taxonomy_term:news_type" => array:11 [ …11]
              "entity:taxonomy_term:tags" => array:11 [ …11]
              "entity:taxonomy_term:tags_youtube" => array:11 [ …11]
              "entity:taxonomy_term:taxonomy_chart_type" => array:11 [ …11]
              "entity:taxonomy_term:topics" => array:11 [ …11]
              "entity:taxonomy_term:training_events" => array:11 [ …11]
              "entity:taxonomy_term:training_tags" => array:11 [ …11]
              "entity:tour" => array:12 [ …12]
              "entity:user" => array:12 [ …12]
              "entity:user_role" => array:12 [ …12]
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              "entity:webform_submission" => array:12 [ …12]
              "entity:webform_submission:aeolus" => array:11 [ …11]
              "entity:webform_submission:application_member_state_short_t" => array:11 [ …11]
              "entity:webform_submission:call_for_external_evaluators" => array:11 [ …11]
              "entity:webform_submission:computing_representatives" => array:11 [ …11]
              "entity:webform_submission:contact" => array:11 [ …11]
              "entity:webform_submission:copernicus_training_expert_eoi" => array:11 [ …11]
              "entity:webform_submission:ecmwf_data_handling_log_traces" => array:11 [ …11]
              "entity:webform_submission:example_options_custom" => array:11 [ …11]
              "entity:webform_submission:keep_for_re_use_dinner_spring_20" => array:11 [ …11]
              "entity:webform_submission:keep_for_re_use_registration_acd" => array:11 [ …11]
              "entity:webform_submission:nominations_for_tac_subgroups" => array:11 [ …11]
              "entity:webform_submission:registration_107th_session_of_th" => array:11 [ …11]
              "entity:webform_submission:registration_108th_session_of_th" => array:11 [ …11]
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              "entity:webform_submission:registration_113th_session_fi" => array:11 [ …11]
              "entity:webform_submission:registration_114th_session_of_th" => array:11 [ …11]
              "entity:webform_submission:registration_29th_session_of_the" => array:11 [ …11]
              "entity:webform_submission:registration_55th_session_of_the" => array:11 [ …11]
              "entity:webform_submission:registration_55th_session_tac" => array:11 [ …11]
              "entity:webform_submission:registration_56th_session_of_the" => array:11 [ …11]
              "entity:webform_submission:registration_56th_session_tac" => array:11 [ …11]
              "entity:webform_submission:registration_57th_session_of_the" => array:11 [ …11]
              "entity:webform_submission:registration_acdp_virtual_meetin" => array:11 [ …11]
              "entity:webform_submission:registration_council_106" => array:11 [ …11]
              "entity:webform_submission:registration_pac_workshop_on_new" => array:11 [ …11]
              "entity:webform_submission:registration_spring_2024_data_po" => array:11 [ …11]
              "entity:webform_submission:special_project_account_registra" => array:11 [ …11]
              "entity:webform_submission:special_project_report_submissio" => array:11 [ …11]
              "entity:webform_submission:special_project_request_submissi" => array:11 [ …11]
              "entity:webform_submission:switchboard" => array:11 [ …11]
              "entity:webform_submission:test" => array:11 [ …11]
              "entity:webform_submission:test_dv" => array:11 [ …11]
              "entity:webform_submission:test_registration_112th_session" => array:11 [ …11]
              "entity:webform_submission:updating_of_ecmwf_s_contact_list" => array:11 [ …11]
              "entity:webform_submission:wmo_fellowship_scheme" => array:11 [ …11]
              "entity:webform" => array:12 [ …12]
              "entity:webform_image_select_images" => array:12 [ …12]
              "entity:webform_options_custom" => array:12 [ …12]
              "entity:webform_protected_downloads" => array:12 [ …12]
              "entity:workflow" => array:12 [ …12]
              "entity:pathauto_pattern" => array:12 [ …12]
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              "entity:paragraph:appoggio_document_fr" => array:11 [ …11]
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              "entity:paragraph:appoggio_last_refresh" => array:11 [ …11]
              "entity:paragraph:appoggio_other" => array:11 [ …11]
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              "entity:paragraph:appoggio_session_row_type" => array:11 [ …11]
              "entity:paragraph:appoggio_title" => array:11 [ …11]
              "entity:paragraph:block_card" => array:11 [ …11]
              "entity:paragraph:card" => array:11 [ …11]
              "entity:paragraph:committee_session_row_files" => array:11 [ …11]
              "entity:paragraph:dataset_parameters_bundle" => array:11 [ …11]
              "entity:paragraph:multilanguage_video" => array:11 [ …11]
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              "entity:paragraph:para_links" => array:11 [ …11]
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              "entity:date_format" => array:12 [ …12]
              "entity:entity_form_display" => array:12 [ …12]
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              "entity:entity_form_mode" => array:12 [ …12]
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              "entity:base_field_override" => array:12 [ …12]
              "entity_reference" => array:8 [ …8]
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              "field_item:block_field" => array:13 [ …13]
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              "field_item:computed_string_long" => array:13 [ …13]
              "field_item:computed_float" => array:13 [ …13]
              "field_item:computed_string" => array:13 [ …13]
              "field_item:computed_integer" => array:13 [ …13]
              "field_item:datetime" => array:14 [ …14]
              "field_item:daterange" => array:13 [ …13]
              "field_item:download_link" => array:14 [ …14]
              "field_item:entity_reference_revisions" => array:13 [ …13]
              "field_item:feeds_item" => array:13 [ …13]
              "field_item:field_collection" => array:15 [ …15]
              "field_item:file_uri" => array:13 [ …13]
              "field_item:file" => array:15 [ …15]
              "field_item:image" => array:16 [ …16]
              "field_item:layout_section" => array:12 [ …12]
              "field_item:link" => array:14 [ …14]
              "field_item:metatag" => array:14 [ …14]
              "field_item:month_year" => array:12 [ …12]
              "field_item:list_integer" => array:14 [ …14]
              "field_item:list_float" => array:14 [ …14]
              "field_item:list_string" => array:14 [ …14]
              "field_item:path" => array:13 [ …13]
              "field_item:redirect_source" => array:13 [ …13]
              "field_item:search_api_exclude_entity" => array:13 [ …13]
              "field_item:smartdate" => array:13 [ …13]
              "field_item:text_with_summary" => array:14 [ …14]
              "field_item:text" => array:14 [ …14]
              "field_item:text_long" => array:14 [ …14]
              "field_item:video_embed_field" => array:14 [ …14]
              "field_item:webform" => array:13 [ …13]
              "field_item:weight" => array:13 [ …13]
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