From 494def108039d937df799a870f10c5c67aba1cb0 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Mon, 13 Feb 2023 10:39:34 -0500 Subject: [PATCH 01/29] Add zarr-accumulation/v1.0.rst draft --- docs/extensions/zarr-accumulation/v1.0.rst | 78 ++++++++++++++++++++++ 1 file changed, 78 insertions(+) create mode 100644 docs/extensions/zarr-accumulation/v1.0.rst diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst new file mode 100644 index 00000000..ef497d78 --- /dev/null +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -0,0 +1,78 @@ +========================================== +Zarr-based Chunk-level Accumulation in Reduced Dimensions (version 1.0) +========================================== + + **Editor's draft 12 02 2023** + +Specification URI: + https://purl.org/zarr/spec/extensions/zarr-accumulation/1.0 + +Corresponding ZEP: + `ZEP 5 — Zarr-based Chunk-level Accumulation in Reduced Dimensions `_ + +Suggest an edit for this spec: + `GitHub editor `_ + +This proposal is licensed under the Apache License, Version 2.0. + +---- + + +Abstract +======== + +At NASA GES DISC, we receive a large number of user requests each day for a variety of analysis and visualization services involving averaging along one or more dimensions, some of which are computationally expensive when running against large amounts of geospatial data. We proposed a generic and dimension-agnostic method based on chunk-level cumulative sums (accumulation) on a regular grid, which provides fast and cost-efficient cloud analysis for multidimensional averaging services. This method introduces a small adjustable set of auxiliary data on top of the raw data, and dramatically reduces the computational time by orders of magnitude based on chunk-level accumulation along one or more dimensions. + +We hereby propose a Zarr extension for this chunk-level accumulation approach. In this proposal, we will present a Zarr group for the accumulation data, a JSON schema for the accumulation group attribute, a JSON schema for the accumulation data array attribute, and an example of the user application interface. +shards. + + +Status of this document +======================= + +.. warning:: + This document is a draft for review and subject to changes. + + +Motivation +========== + +Performing the averaging operation over data in Zarr generally requires a full scan of the data. This can be parallelized with Dask (or any other distributed framework), but reading all of the data is an unavoidable bottleneck. Our proposed approach, Zarr-based Chunk-level Accumulation, will improve the speed and cost of long-range calculation by loading only a few data chunks at the averaging boundary. Here, we provide examples of how the approach is applied to geospatial data with temporal and spatial dimensions; however, it’s noteworthy that this approach is dimension-agnostic and can be generalized for all types of multidimensional data aggregation services with Zarr. + + +Document conventions +==================== + +Conformance requirements are expressed with a combination of descriptive +assertions and [RFC2119]_ terminology. The key words "MUST", "MUST NOT", +"REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", +and "OPTIONAL" in the normative parts of this document are to be interpreted as +described in [RFC2119]_. However, for readability, these words do not appear in +all uppercase letters in this specification. + +All of the text of this specification is normative except sections explicitly +marked as non-normative, examples, and notes. Examples in this specification are +introduced with the words "for example". + + +Implementation +================================== + +Zarr group structure of accumulation data +-------------------------- + + + +References +========== + +.. [RFC2119] S. Bradner. Key words for use in RFCs to Indicate + Requirement Levels. March 1997. Best Current Practice. URL: + https://tools.ietf.org/html/rfc2119 + + +Change log +========== + +This section is a placeholder for keeping a log of the snapshots of this +document that are tagged in GitHub and what changed between them. From a31ce728e57c51ae1b0bd6259a726fe49e24dfba Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Mon, 13 Feb 2023 21:00:05 -0500 Subject: [PATCH 02/29] zarr-accumulation.rst added --- docs/extensions/zarr-accumulation.rst | 13 +++++++++++++ 1 file changed, 13 insertions(+) create mode 100644 docs/extensions/zarr-accumulation.rst diff --git a/docs/extensions/zarr-accumulation.rst b/docs/extensions/zarr-accumulation.rst new file mode 100644 index 00000000..56cd6aae --- /dev/null +++ b/docs/extensions/zarr-accumulation.rst @@ -0,0 +1,13 @@ +==================== +Zarr-based Chunk-level Accumulation in Reduced Dimensions +==================== + +Under construction. + +.. toctree:: + :glob: + :maxdepth: 1 + :titlesonly: + :caption: Contents: + + zarr-accumulation/* From 64dc8734a581a3a64b667f0e2c96e9a31f4b8845 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Mon, 13 Feb 2023 21:04:33 -0500 Subject: [PATCH 03/29] zarr-accumulation/v1.0.rst more content added --- docs/extensions/zarr-accumulation/v1.0.rst | 27 ++++++++++++++++++++++ 1 file changed, 27 insertions(+) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index ef497d78..d57e3710 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -58,9 +58,36 @@ introduced with the words "for example". Implementation ================================== +We propose to formalize this Zarr-based Chunk-level Accumulation approach as a Zarr extension. To implement this approach, cumulative sums are computed at chunk intervals and are stored in a Zarr group. The API for averaging the data fetches the necessary pre-computed sums based on the user-requested dimensions (e.g., time) and dimension ranges (e.g., from 1980 to 1990). + +Please note that this solution is also applicable for storing chunk statistics (min, max, sum, count, etc.) to help with performing aggregations. + Zarr group structure of accumulation data -------------------------- +Rather than storing the chunk-level statistics in a separate store, we could store them inline with the arrays they are derived from. This would enable other applications to take advantage of such pre-computed data to optimize queries. This is similar to an optimization in Snowflake ([twitter link](https://twitter.com/teej_m/status/1546591452750159873)). + +The accumulation datasets are organized in a data group adjacent to the raw data and dimension arrays with the following structure: + +.. code-block:: + +├── ${dimension_array} +├── ... +├── ${raw_dataset} +├── ... +└── ${raw_dataset}_accumulation_group + ├── .zgroup + ├── .zattr + ├── ${accumulation_dataset_1} + │ ├── .zarray + │ ├── .zattr + │ └── ... + ├── ${accumulation_dataset_2} + │ ├── .zarray + │ ├── .zattr + │ └── ... + ... + References From 169056327f8820a531f992c249a026c5f144a6f2 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Mon, 13 Feb 2023 21:08:58 -0500 Subject: [PATCH 04/29] zarr-accumulation/v1.0.rst hyperlink polished --- docs/extensions/zarr-accumulation/v1.0.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index d57e3710..73348439 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -65,7 +65,7 @@ Please note that this solution is also applicable for storing chunk statistics ( Zarr group structure of accumulation data -------------------------- -Rather than storing the chunk-level statistics in a separate store, we could store them inline with the arrays they are derived from. This would enable other applications to take advantage of such pre-computed data to optimize queries. This is similar to an optimization in Snowflake ([twitter link](https://twitter.com/teej_m/status/1546591452750159873)). +Rather than storing the chunk-level statistics in a separate store, we could store them inline with the arrays they are derived from. This would enable other applications to take advantage of such pre-computed data to optimize queries. This is similar to an optimization in Snowflake (`twitter link `_). The accumulation datasets are organized in a data group adjacent to the raw data and dimension arrays with the following structure: From 412a4405f82d8112ca5946024a0f601ab4640e92 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Mon, 13 Feb 2023 21:10:01 -0500 Subject: [PATCH 05/29] zarr-accumulation/v1.0.rst minor cleaning --- docs/extensions/zarr-accumulation/v1.0.rst | 1 - 1 file changed, 1 deletion(-) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index 73348439..f18593c2 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -24,7 +24,6 @@ Abstract At NASA GES DISC, we receive a large number of user requests each day for a variety of analysis and visualization services involving averaging along one or more dimensions, some of which are computationally expensive when running against large amounts of geospatial data. We proposed a generic and dimension-agnostic method based on chunk-level cumulative sums (accumulation) on a regular grid, which provides fast and cost-efficient cloud analysis for multidimensional averaging services. This method introduces a small adjustable set of auxiliary data on top of the raw data, and dramatically reduces the computational time by orders of magnitude based on chunk-level accumulation along one or more dimensions. We hereby propose a Zarr extension for this chunk-level accumulation approach. In this proposal, we will present a Zarr group for the accumulation data, a JSON schema for the accumulation group attribute, a JSON schema for the accumulation data array attribute, and an example of the user application interface. -shards. Status of this document From bc022eabac327bed5ae8a6454244ef1add038997 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 12:40:59 -0500 Subject: [PATCH 06/29] zarr-accumulation/v1.0.rst code formatting --- docs/extensions/zarr-accumulation/v1.0.rst | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index f18593c2..75e07929 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -68,8 +68,7 @@ Rather than storing the chunk-level statistics in a separate store, we could sto The accumulation datasets are organized in a data group adjacent to the raw data and dimension arrays with the following structure: -.. code-block:: - +`` ├── ${dimension_array} ├── ... ├── ${raw_dataset} @@ -86,7 +85,7 @@ The accumulation datasets are organized in a data group adjacent to the raw data │ ├── .zattr │ └── ... ... - +`` References From e1c4412c5a63597fc61319de531196e10075810d Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 12:43:26 -0500 Subject: [PATCH 07/29] zarr-accumulation/v1.0.rst code formatting --- docs/extensions/zarr-accumulation/v1.0.rst | 38 ++++++++++++---------- 1 file changed, 20 insertions(+), 18 deletions(-) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index 75e07929..cbb245be 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -68,24 +68,26 @@ Rather than storing the chunk-level statistics in a separate store, we could sto The accumulation datasets are organized in a data group adjacent to the raw data and dimension arrays with the following structure: -`` -├── ${dimension_array} -├── ... -├── ${raw_dataset} -├── ... -└── ${raw_dataset}_accumulation_group - ├── .zgroup - ├── .zattr - ├── ${accumulation_dataset_1} - │ ├── .zarray - │ ├── .zattr - │ └── ... - ├── ${accumulation_dataset_2} - │ ├── .zarray - │ ├── .zattr - │ └── ... - ... -`` +.. code-block:: + + ├── ${dimension_array} + ├── ... + ├── ${raw_dataset} + ├── ... + └── ${raw_dataset}_accumulation_group + ├── .zgroup + ├── .zattr + ├── ${accumulation_dataset_1} + │ ├── .zarray + │ ├── .zattr + │ └── ... + ├── ${accumulation_dataset_2} + │ ├── .zarray + │ ├── .zattr + │ └── ... + ... + +Done References From 6887e225df4db20753d694557d92def940340374 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 12:45:10 -0500 Subject: [PATCH 08/29] zarr-accumulation/v1.0.rst more content added --- docs/extensions/zarr-accumulation/v1.0.rst | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index cbb245be..c4b2be39 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -87,8 +87,7 @@ The accumulation datasets are organized in a data group adjacent to the raw data │ └── ... ... -Done - +where `${dimension_array}`` is the data array for the dimension variable, `${raw_dataset}` is the data array for the raw dataset, `${raw_dataset}_accumulation_group` is the group for accumulation, and `${accumulation_dataset_1}` and `${accumulation_dataset_2}` are the data arrays for each accumulation dataset. References ========== From 4f6eeda1b9110ace5ee9caf523ce55ad009898ab Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 12:46:46 -0500 Subject: [PATCH 09/29] zarr-accumulation/v1.0.rst code formatting --- docs/extensions/zarr-accumulation/v1.0.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index c4b2be39..6f886d72 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -87,7 +87,7 @@ The accumulation datasets are organized in a data group adjacent to the raw data │ └── ... ... -where `${dimension_array}`` is the data array for the dimension variable, `${raw_dataset}` is the data array for the raw dataset, `${raw_dataset}_accumulation_group` is the group for accumulation, and `${accumulation_dataset_1}` and `${accumulation_dataset_2}` are the data arrays for each accumulation dataset. +where ``${dimension_array}`` is the data array for the dimension variable, ``${raw_dataset}`` is the data array for the raw dataset, ``${raw_dataset}_accumulation_group`` is the group for accumulation, and ``${accumulation_dataset_1}`` and ``${accumulation_dataset_2}`` are the data arrays for each accumulation dataset. References ========== From 63b889705441c090f942f1b5b550126260409a14 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 12:50:13 -0500 Subject: [PATCH 10/29] zarr-accumulation/v1.0.rst more content added --- docs/extensions/zarr-accumulation/v1.0.rst | 8 +++++++- 1 file changed, 7 insertions(+), 1 deletion(-) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index 6f886d72..62d8bc8f 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -68,7 +68,7 @@ Rather than storing the chunk-level statistics in a separate store, we could sto The accumulation datasets are organized in a data group adjacent to the raw data and dimension arrays with the following structure: -.. code-block:: +group structure:: ├── ${dimension_array} ├── ... @@ -89,6 +89,12 @@ The accumulation datasets are organized in a data group adjacent to the raw data where ``${dimension_array}`` is the data array for the dimension variable, ``${raw_dataset}`` is the data array for the raw dataset, ``${raw_dataset}_accumulation_group`` is the group for accumulation, and ``${accumulation_dataset_1}`` and ``${accumulation_dataset_2}`` are the data arrays for each accumulation dataset. +Zarr attribute file of accumulation group +-------------------------- + +The accumulation group attribute file, ``${raw_dataset}_accumulation_group/.zattr``, provides details of the accumulation implementation and data organization. It follows the JSON schema shown below: + + References ========== From 6329a42d82065f8b20fa052b76082a705dfb6648 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 12:51:00 -0500 Subject: [PATCH 11/29] zarr-accumulation/v1.0.rst code formatting --- docs/extensions/zarr-accumulation/v1.0.rst | 4 +--- 1 file changed, 1 insertion(+), 3 deletions(-) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index 62d8bc8f..5a11d159 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -66,9 +66,7 @@ Zarr group structure of accumulation data Rather than storing the chunk-level statistics in a separate store, we could store them inline with the arrays they are derived from. This would enable other applications to take advantage of such pre-computed data to optimize queries. This is similar to an optimization in Snowflake (`twitter link `_). -The accumulation datasets are organized in a data group adjacent to the raw data and dimension arrays with the following structure: - -group structure:: +The accumulation datasets are organized in a data group adjacent to the raw data and dimension arrays with the following structure::: ├── ${dimension_array} ├── ... From b4890217107a03d965e3f0775c1506b3e87c04c8 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 12:52:24 -0500 Subject: [PATCH 12/29] zarr-accumulation/v1.0.rst code formatting --- docs/extensions/zarr-accumulation/v1.0.rst | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index 5a11d159..509031c6 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -66,7 +66,8 @@ Zarr group structure of accumulation data Rather than storing the chunk-level statistics in a separate store, we could store them inline with the arrays they are derived from. This would enable other applications to take advantage of such pre-computed data to optimize queries. This is similar to an optimization in Snowflake (`twitter link `_). -The accumulation datasets are organized in a data group adjacent to the raw data and dimension arrays with the following structure::: +The accumulation datasets are organized in a data group adjacent to the raw data and dimension arrays with the following structure: +.. code-block:: ├── ${dimension_array} ├── ... From 7b40c0044d92c1126aa33bc4e6de6c7ea7274d2e Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 12:53:09 -0500 Subject: [PATCH 13/29] zarr-accumulation/v1.0.rst code formatting --- docs/extensions/zarr-accumulation/v1.0.rst | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index 509031c6..5f2b3b23 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -66,8 +66,7 @@ Zarr group structure of accumulation data Rather than storing the chunk-level statistics in a separate store, we could store them inline with the arrays they are derived from. This would enable other applications to take advantage of such pre-computed data to optimize queries. This is similar to an optimization in Snowflake (`twitter link `_). -The accumulation datasets are organized in a data group adjacent to the raw data and dimension arrays with the following structure: -.. code-block:: +The accumulation datasets are organized in a data group adjacent to the raw data and dimension arrays with the following structure: :: ├── ${dimension_array} ├── ... From e76ed28528efefb020d5d694b9c7365c59e55ed6 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 12:54:24 -0500 Subject: [PATCH 14/29] zarr-accumulation/v1.0.rst more content added --- docs/extensions/zarr-accumulation/v1.0.rst | 42 +++++++++++++++++++++- 1 file changed, 41 insertions(+), 1 deletion(-) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index 5f2b3b23..226667ae 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -90,7 +90,47 @@ where ``${dimension_array}`` is the data array for the dimension variable, ``${r Zarr attribute file of accumulation group -------------------------- -The accumulation group attribute file, ``${raw_dataset}_accumulation_group/.zattr``, provides details of the accumulation implementation and data organization. It follows the JSON schema shown below: +The accumulation group attribute file, ``${raw_dataset}_accumulation_group/.zattr``, provides details of the accumulation implementation and data organization. It follows the JSON schema shown below: :: + { + "$schema": "http://json-schema.org/draft-07/schema#", + "type": "object", + "definitions": { + "accumulation_data_array": { + "type": "object", + "properties": { + "_DATA_UNWEIGHTED": { + "type": "string" + }, + "_DATA_WEIGHTED": { + "type": "string" + }, + "_WEIGHTS": { + "type": "string" + } + }, + "patternProperties": { + "^(?!_DATA_UNWEIGHTED|_DATA_WEIGHTED|_WEIGHTS).*$": { + "$ref": "#/definitions/accumulation_data_array" + } + }, + "additionalProperties": false + } + }, + "properties": { + "_ACCUMULATION_GROUP": { + "type": "object", + "patternProperties": { + "^(?!_DATA_UNWEIGHTED|_DATA_WEIGHTED|_WEIGHTS).*$": { + "$ref": "#/definitions/accumulation_data_array" + } + }, + "additionalProperties": false + } + }, + "required": [ + "_ACCUMULATION_GROUP" + ] + } References From 800ff959e1a6f80a385fedd8c081b82755232c28 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 12:55:22 -0500 Subject: [PATCH 15/29] zarr-accumulation/v1.0.rst more content added --- docs/extensions/zarr-accumulation/v1.0.rst | 1 + 1 file changed, 1 insertion(+) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index 226667ae..5c1ab489 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -91,6 +91,7 @@ Zarr attribute file of accumulation group -------------------------- The accumulation group attribute file, ``${raw_dataset}_accumulation_group/.zattr``, provides details of the accumulation implementation and data organization. It follows the JSON schema shown below: :: + { "$schema": "http://json-schema.org/draft-07/schema#", "type": "object", From ac27f9f659a30d6b6326c9c57ea5226fa5495403 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 13:02:17 -0500 Subject: [PATCH 16/29] zarr-accumulation/v1.0.rst more content added --- docs/extensions/zarr-accumulation/v1.0.rst | 28 ++++++++++++++++++++++ 1 file changed, 28 insertions(+) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index 5c1ab489..ff011738 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -134,6 +134,34 @@ The accumulation group attribute file, ``${raw_dataset}_accumulation_group/.zatt } +The recursive definition (`#/definitions/accumulation_data_array`) under the schema root (`_ACCUMULATION_GROUP`) provides details of the cumulative sum statistics, including the dataset names, accumulation types and dimensions. The keys of its `properties` (`_DATA_UNWEIGHTED`, `_DATA_WEIGHTED`, and `_WEIGHTS`) indicate the cumulative sum types (for unweighted data, weighted data, and weights respectively), whereas its values give the cumulative sum dataset names. The accumulation dimension names are saved in the keys of its `patternProperties` along the recursion chain; it is noteworthy that these dimension names need to be ordered to avoid ambiguity and redundancy. + +An example of the above zarr attribute file is given as follows. The data has three dimensions including *latitude*, *longitude* and *time*. The cumulative sums are computed for the weighted data (`_DATA_WEIGHTED`) and weights (`_WEIGHTS`). If we want to provide the time-averaged map and area-averaged time series, the accumulation is only needed for the dimension combinations of *latitude*, *longitude*, *time*, and *latitude*+*longitude*; all other dimension combinations (e.g. *latitude*+*time*, *longitude*+*time*, and *latitude*+*longitude*+*time*) are empty (`{}`). :: + + { + "_ACCUMULATION_GROUP": { + "latitude": { + "_DATA_WEIGHTED": "acc_lat", + "_WEIGHTS": "acc_wt_lat", + "longitude": { + "_DATA_WEIGHTED": "acc_lat_lon", + "_WEIGHTS": "acc_wt_lat_lon", + "time": {} + }, + "time": {} + }, + "longitude": { + "_DATA_WEIGHTED": "acc_lon", + "_WEIGHTS": "acc_wt_lon", + "time": {} + }, + "time": { + "_DATA_WEIGHTED": "acc_time", + "_WEIGHTS": "acc_wt_time" + } + } + } + References ========== From ec3ac00b21a0518b26042145963b257bb1d396f2 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 13:03:41 -0500 Subject: [PATCH 17/29] zarr-accumulation/v1.0.rst more content added --- docs/extensions/zarr-accumulation/v1.0.rst | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index ff011738..e7fa1b60 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -134,9 +134,9 @@ The accumulation group attribute file, ``${raw_dataset}_accumulation_group/.zatt } -The recursive definition (`#/definitions/accumulation_data_array`) under the schema root (`_ACCUMULATION_GROUP`) provides details of the cumulative sum statistics, including the dataset names, accumulation types and dimensions. The keys of its `properties` (`_DATA_UNWEIGHTED`, `_DATA_WEIGHTED`, and `_WEIGHTS`) indicate the cumulative sum types (for unweighted data, weighted data, and weights respectively), whereas its values give the cumulative sum dataset names. The accumulation dimension names are saved in the keys of its `patternProperties` along the recursion chain; it is noteworthy that these dimension names need to be ordered to avoid ambiguity and redundancy. +The recursive definition (``#/definitions/accumulation_data_array``) under the schema root (``_ACCUMULATION_GROUP``) provides details of the cumulative sum statistics, including the dataset names, accumulation types and dimensions. The keys of its ``properties`` (``_DATA_UNWEIGHTED``, ``_DATA_WEIGHTED``, and ``_WEIGHTS``) indicate the cumulative sum types (for unweighted data, weighted data, and weights respectively), whereas its values give the cumulative sum dataset names. The accumulation dimension names are saved in the keys of its ``patternProperties`` along the recursion chain; it is noteworthy that these dimension names need to be ordered to avoid ambiguity and redundancy. -An example of the above zarr attribute file is given as follows. The data has three dimensions including *latitude*, *longitude* and *time*. The cumulative sums are computed for the weighted data (`_DATA_WEIGHTED`) and weights (`_WEIGHTS`). If we want to provide the time-averaged map and area-averaged time series, the accumulation is only needed for the dimension combinations of *latitude*, *longitude*, *time*, and *latitude*+*longitude*; all other dimension combinations (e.g. *latitude*+*time*, *longitude*+*time*, and *latitude*+*longitude*+*time*) are empty (`{}`). :: +An example of the above zarr attribute file is given as follows. The data has three dimensions including *latitude*, *longitude* and *time*. The cumulative sums are computed for the weighted data (``_DATA_WEIGHTED``) and weights (``_WEIGHTS``). If we want to provide the time-averaged map and area-averaged time series, the accumulation is only needed for the dimension combinations of *latitude*, *longitude*, *time*, and *latitude*+*longitude*; all other dimension combinations (e.g. *latitude*+*time*, *longitude*+*time*, and *latitude*+*longitude*+*time*) are empty (``{}``). :: { "_ACCUMULATION_GROUP": { From 4030f3609366edca0f17a63480dcea64facecf93 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 13:05:44 -0500 Subject: [PATCH 18/29] zarr-accumulation/v1.0.rst code formatting --- docs/extensions/zarr-accumulation/v1.0.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index e7fa1b60..da20f3d0 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -136,7 +136,7 @@ The accumulation group attribute file, ``${raw_dataset}_accumulation_group/.zatt The recursive definition (``#/definitions/accumulation_data_array``) under the schema root (``_ACCUMULATION_GROUP``) provides details of the cumulative sum statistics, including the dataset names, accumulation types and dimensions. The keys of its ``properties`` (``_DATA_UNWEIGHTED``, ``_DATA_WEIGHTED``, and ``_WEIGHTS``) indicate the cumulative sum types (for unweighted data, weighted data, and weights respectively), whereas its values give the cumulative sum dataset names. The accumulation dimension names are saved in the keys of its ``patternProperties`` along the recursion chain; it is noteworthy that these dimension names need to be ordered to avoid ambiguity and redundancy. -An example of the above zarr attribute file is given as follows. The data has three dimensions including *latitude*, *longitude* and *time*. The cumulative sums are computed for the weighted data (``_DATA_WEIGHTED``) and weights (``_WEIGHTS``). If we want to provide the time-averaged map and area-averaged time series, the accumulation is only needed for the dimension combinations of *latitude*, *longitude*, *time*, and *latitude*+*longitude*; all other dimension combinations (e.g. *latitude*+*time*, *longitude*+*time*, and *latitude*+*longitude*+*time*) are empty (``{}``). :: +An example of the above zarr attribute file is given as follows. The data has three dimensions including *latitude*, *longitude* and *time*. The cumulative sums are computed for the weighted data (``_DATA_WEIGHTED``) and weights (``_WEIGHTS``). If we want to provide the time-averaged map and area-averaged time series, the accumulation is only needed for the dimension combinations of *latitude*, *longitude*, *time*, and *latitude+longitude*; all other dimension combinations (e.g. *latitude+time*, *longitude+time*, and *latitude+longitude+time*) are empty (``{}``). :: { "_ACCUMULATION_GROUP": { From dc1e5599ff55306c386210c0eb1397eb1a815fc7 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 13:25:18 -0500 Subject: [PATCH 19/29] zarr-accumulation/v1.0.rst more content added --- docs/extensions/zarr-accumulation/v1.0.rst | 62 ++++++++++++++++++++++ 1 file changed, 62 insertions(+) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index da20f3d0..bfb1a0a7 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -162,6 +162,68 @@ An example of the above zarr attribute file is given as follows. The data has t } } +Zarr attribute file of accumulation data array +-------------------------- + + +With Zarr-based chunk-level accumulation, the cumulative sums are not necessarily computed for every single chunk. To further reduce the computation and storage cost for the accumulation data, the cumulative sums can be computed every certain number of chunks, and we call this tunable number the *accumulation stride*. This information is saved in the Zarr attribute file for the accumulation dataset (e.g., ``${raw_dataset}_accumulation_group/{accumulation_dataset_1}/.zattr``). + +As mentioned above, the dimension labels are needed to identify the accumulation datasets. We assume that the dimensions are defined in the attributes of the dataset as ``_ARRAY_DIMENSIONS`` as from [the xarray implementation](https://docs.xarray.dev/en/stable/internals/zarr-encoding-spec.html). In the present approach, the accumulation stride is saved in an object called ``_ACCUMULATION_STRIDE`` in parallel with ``_ARRAY_DIMENSIONS``. The related schema segment of this attribute file is shown as follows: :: + { + "$schema":"http://json-schema.org/draft-07/schema#", + "type":"object", + "properties":{ + "_ARRAY_DIMENSIONS":{ + "type":"array", + "items":{ + "type":"string" + } + }, + "_ACCUMULATION_STRIDE":{ + "type":"array", + "items":{ + "type":"integer" + } + } + }, + "required":[ + "_ARRAY_DIMENSIONS", + "_ACCUMULATION_STRIDE" + ] + } + +The ``_ARRAY_DIMENSIONS`` and ``_ACCUMULATION_STRIDE`` arrays should have the same length. Each item in the ``_ACCUMULATION_STRIDE`` array represents the accumulation stride along the dimension from the ``_ARRAY_DIMENSIONS`` array at the same index. The value of accumulation stride should be a non-negative integer: a positive value represents the accumulation stride as defined above, whereas a value of 0 indicates the accumulation is not performed along the given dimension. + +For example, the following attribute file represents the accumulation that is performed along only the time dimension every other chunk: :: + + { + "_ARRAY_DIMENSIONS":[ + "latitude", + "longitude", + "time" + ], + "_ACCUMULATION_STRIDE":[ + 0, + 0, + 2 + ] + } + +and the following attribute file represents the accumulation that is performed along the latitude dimension for each chunk, and along longitude dimension every 3 chunks: :: + + { + "_ARRAY_DIMENSIONS":[ + "latitude", + "longitude", + "time" + ], + "_ACCUMULATION_STRIDE":[ + 1, + 3, + 0 + ] + } + References ========== From 5ddad6754002b3cc68265baf647cb04115e0dd91 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 13:27:08 -0500 Subject: [PATCH 20/29] zarr-accumulation/v1.0.rst code formatting --- docs/extensions/zarr-accumulation/v1.0.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index bfb1a0a7..f4541895 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -168,7 +168,7 @@ Zarr attribute file of accumulation data array With Zarr-based chunk-level accumulation, the cumulative sums are not necessarily computed for every single chunk. To further reduce the computation and storage cost for the accumulation data, the cumulative sums can be computed every certain number of chunks, and we call this tunable number the *accumulation stride*. This information is saved in the Zarr attribute file for the accumulation dataset (e.g., ``${raw_dataset}_accumulation_group/{accumulation_dataset_1}/.zattr``). -As mentioned above, the dimension labels are needed to identify the accumulation datasets. We assume that the dimensions are defined in the attributes of the dataset as ``_ARRAY_DIMENSIONS`` as from [the xarray implementation](https://docs.xarray.dev/en/stable/internals/zarr-encoding-spec.html). In the present approach, the accumulation stride is saved in an object called ``_ACCUMULATION_STRIDE`` in parallel with ``_ARRAY_DIMENSIONS``. The related schema segment of this attribute file is shown as follows: :: +As mentioned above, the dimension labels are needed to identify the accumulation datasets. We assume that the dimensions are defined in the attributes of the dataset as ``_ARRAY_DIMENSIONS`` as from `the xarray implementation `_. In the present approach, the accumulation stride is saved in an object called ``_ACCUMULATION_STRIDE`` in parallel with ``_ARRAY_DIMENSIONS``. The related schema segment of this attribute file is shown as follows: :: { "$schema":"http://json-schema.org/draft-07/schema#", "type":"object", From 4181d854cbf48e9903cd64108bfa84b016813258 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 13:27:44 -0500 Subject: [PATCH 21/29] zarr-accumulation/v1.0.rst code formatting --- docs/extensions/zarr-accumulation/v1.0.rst | 1 + 1 file changed, 1 insertion(+) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index f4541895..279e7fbc 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -169,6 +169,7 @@ Zarr attribute file of accumulation data array With Zarr-based chunk-level accumulation, the cumulative sums are not necessarily computed for every single chunk. To further reduce the computation and storage cost for the accumulation data, the cumulative sums can be computed every certain number of chunks, and we call this tunable number the *accumulation stride*. This information is saved in the Zarr attribute file for the accumulation dataset (e.g., ``${raw_dataset}_accumulation_group/{accumulation_dataset_1}/.zattr``). As mentioned above, the dimension labels are needed to identify the accumulation datasets. We assume that the dimensions are defined in the attributes of the dataset as ``_ARRAY_DIMENSIONS`` as from `the xarray implementation `_. In the present approach, the accumulation stride is saved in an object called ``_ACCUMULATION_STRIDE`` in parallel with ``_ARRAY_DIMENSIONS``. The related schema segment of this attribute file is shown as follows: :: + { "$schema":"http://json-schema.org/draft-07/schema#", "type":"object", From be5a3aad40f2cc92d511444531805a60828651c9 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 14:14:05 -0500 Subject: [PATCH 22/29] zarr-accumulation/v1.0.rst more content added --- .../Zarr_accumulation-App_Interface-1.png | Bin 0 -> 260995 bytes .../Zarr_accumulation-App_Interface-2.png | Bin 0 -> 179477 bytes docs/extensions/zarr-accumulation/v1.0.rst | 11 +++++++++++ 3 files changed, 11 insertions(+) create mode 100644 docs/extensions/zarr-accumulation/Zarr_accumulation-App_Interface-1.png create mode 100644 docs/extensions/zarr-accumulation/Zarr_accumulation-App_Interface-2.png diff --git a/docs/extensions/zarr-accumulation/Zarr_accumulation-App_Interface-1.png b/docs/extensions/zarr-accumulation/Zarr_accumulation-App_Interface-1.png new file mode 100644 index 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The accumulation data array name for the given dimensions can be obtained from the accumulation group attributes. The following example shows the steps to get the weighted accumulation data array name along *latitude+longitude* dimensions: + +.. image:: Zarr_accumulation-App_Interface-1.png + +The accumulation stride is also needed to locate the accumulation data for a given chunk number. They can be obtained from the accumulation data attributes, and the following example shows the steps to get the accumulation stride for the accumulation data along *latitude+longitude* dimensions: + +.. image:: Zarr_accumulation-App_Interface-2.png + + References ========== From 27ecba51fd3e60a326e944d74b47ad0823cc996a Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 14:52:57 -0500 Subject: [PATCH 23/29] more content added in Motivation --- docs/extensions/zarr-accumulation/v1.0.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index 43d79e62..3049f9ec 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -36,7 +36,7 @@ Status of this document Motivation ========== -Performing the averaging operation over data in Zarr generally requires a full scan of the data. This can be parallelized with Dask (or any other distributed framework), but reading all of the data is an unavoidable bottleneck. Our proposed approach, Zarr-based Chunk-level Accumulation, will improve the speed and cost of long-range calculation by loading only a few data chunks at the averaging boundary. Here, we provide examples of how the approach is applied to geospatial data with temporal and spatial dimensions; however, it’s noteworthy that this approach is dimension-agnostic and can be generalized for all types of multidimensional data aggregation services with Zarr. +At NASA GES DISC, our use case is for computing averages along a range of data dimensions (e.g., space, time) in a cost effective and highly performant manner. In the Geo-spatial community, computing area or temporal averages over a long range of observations is popular with users. Performing the averaging operation over data in Zarr generally requires a full scan of the data. This can be parallelized with Dask (or any other distributed framework), but reading all of the data is an unavoidable bottleneck. Our proposed approach, Zarr-based Chunk-level Accumulation, will improve the speed and cost of long-range calculation by loading only a few data chunks at the averaging boundary. Here, we provide examples of how the approach is applied to geospatial data with temporal and spatial dimensions; however, it’s noteworthy that this approach is dimension-agnostic and can be generalized for all types of multidimensional data aggregation services with Zarr. Document conventions From 68bf791a53341f137b19a898f885e685212cbcb3 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 15:01:36 -0500 Subject: [PATCH 24/29] Detailed description added --- docs/extensions/zarr-accumulation/v1.0.rst | 11 +++++++++++ 1 file changed, 11 insertions(+) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index 3049f9ec..d8cb0f4f 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -53,6 +53,17 @@ All of the text of this specification is normative except sections explicitly marked as non-normative, examples, and notes. Examples in this specification are introduced with the words "for example". +Detailed description +================================== + +The fundamental of this Zarr-based Chunk-level Accumulation algorithm is to pre-compute `cumulative sums `_ of data values and weights/counts along data dimensions at the chunk intervals. These cumulative sums can then be used to find data averages for dimension ranges. + +Example: + +For a sequence `A=(a, b, c, d)`, the cumulative sums are `S=(s0, s1, s2, s3)` where `s0=a, s1=a+b, s2=a+b+c, s3=a+b+c+d`. The average of the sequence over a range can now be calculated using the cumulative sums. For example, assuming zero-based indexing, average `(A[1:])=(S[3]-S[0])/3=(s3-s0)/3`. + +The above example can be extended and generalized for multiple dimensions. This makes the problem of computing averages *O(1)* vs *O(N^m)* for the dimensions being averaged, where *N* is the number of data values and *m* is the number of dimensions to be averaged. See our `ESIP 2022 presentation `_ (and the `slides `_) for a more detailed description. + Implementation ================================== From 82c29485d13658832be6393d9b949770482175d3 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 15:02:29 -0500 Subject: [PATCH 25/29] minor cleaning --- docs/extensions/zarr-accumulation/v1.0.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index d8cb0f4f..04566524 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -58,7 +58,7 @@ Detailed description The fundamental of this Zarr-based Chunk-level Accumulation algorithm is to pre-compute `cumulative sums `_ of data values and weights/counts along data dimensions at the chunk intervals. These cumulative sums can then be used to find data averages for dimension ranges. -Example: +For example: For a sequence `A=(a, b, c, d)`, the cumulative sums are `S=(s0, s1, s2, s3)` where `s0=a, s1=a+b, s2=a+b+c, s3=a+b+c+d`. The average of the sequence over a range can now be calculated using the cumulative sums. For example, assuming zero-based indexing, average `(A[1:])=(S[3]-S[0])/3=(s3-s0)/3`. From 0d2e1e7f72119896dbae98cf79feb11eb982ddce Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 15:03:34 -0500 Subject: [PATCH 26/29] minor cleaning --- docs/extensions/zarr-accumulation/v1.0.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index 04566524..565f9a8f 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -60,7 +60,7 @@ The fundamental of this Zarr-based Chunk-level Accumulation algorithm is to pre- For example: -For a sequence `A=(a, b, c, d)`, the cumulative sums are `S=(s0, s1, s2, s3)` where `s0=a, s1=a+b, s2=a+b+c, s3=a+b+c+d`. The average of the sequence over a range can now be calculated using the cumulative sums. For example, assuming zero-based indexing, average `(A[1:])=(S[3]-S[0])/3=(s3-s0)/3`. +For a sequence ``A=(a, b, c, d)``, the cumulative sums are ``S=(s0, s1, s2, s3)`` where ``s0=a, s1=a+b, s2=a+b+c, s3=a+b+c+d``. The average of the sequence over a range can now be calculated using the cumulative sums. For example, assuming zero-based indexing, average ``(A[1:])=(S[3]-S[0])/3=(s3-s0)/3``. The above example can be extended and generalized for multiple dimensions. This makes the problem of computing averages *O(1)* vs *O(N^m)* for the dimensions being averaged, where *N* is the number of data values and *m* is the number of dimensions to be averaged. See our `ESIP 2022 presentation `_ (and the `slides `_) for a more detailed description. From 87f3d70c82e5d36ff6de15e2782f5d582620bf12 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 15:18:26 -0500 Subject: [PATCH 27/29] minor cleaning --- docs/extensions/zarr-accumulation/v1.0.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index 565f9a8f..44975a11 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -179,7 +179,7 @@ Zarr attribute file of accumulation data array With Zarr-based chunk-level accumulation, the cumulative sums are not necessarily computed for every single chunk. To further reduce the computation and storage cost for the accumulation data, the cumulative sums can be computed every certain number of chunks, and we call this tunable number the *accumulation stride*. This information is saved in the Zarr attribute file for the accumulation dataset (e.g., ``${raw_dataset}_accumulation_group/{accumulation_dataset_1}/.zattr``). -As mentioned above, the dimension labels are needed to identify the accumulation datasets. We assume that the dimensions are defined in the attributes of the dataset as ``_ARRAY_DIMENSIONS`` as from `the xarray implementation `_. In the present approach, the accumulation stride is saved in an object called ``_ACCUMULATION_STRIDE`` in parallel with ``_ARRAY_DIMENSIONS``. The related schema segment of this attribute file is shown as follows: :: +As mentioned above, the dimension labels are needed to identify the accumulation datasets. We assume that the dimensions are defined in the attributes of the dataset as ``_ARRAY_DIMENSIONS`` as from `the xarray implementation `_. In the present approach, the *accumulation stride* is saved in an object called ``_ACCUMULATION_STRIDE`` in parallel with ``_ARRAY_DIMENSIONS``. The related schema segment of this attribute file is shown as follows: :: { "$schema":"http://json-schema.org/draft-07/schema#", From d6da2f2f0e0bc50d4a1b859b5f770ffb378d62da Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 15:21:17 -0500 Subject: [PATCH 28/29] minor cleaning --- docs/extensions/zarr-accumulation/v1.0.rst | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index 44975a11..3d2e990e 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -236,7 +236,8 @@ and the following attribute file represents the accumulation that is performed a ] } -### Application Interface +Application Interface +-------------------------- The accumulation-based workflow requires the application to locate the accumulation data along certain dimensions. The accumulation data array name for the given dimensions can be obtained from the accumulation group attributes. The following example shows the steps to get the weighted accumulation data array name along *latitude+longitude* dimensions: From c302847de9177d94b6044f46b2e532734162c2a1 Mon Sep 17 00:00:00 2001 From: Hailiang Zhang Date: Tue, 14 Feb 2023 15:31:03 -0500 Subject: [PATCH 29/29] hyperlink provided --- docs/extensions/zarr-accumulation/v1.0.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/extensions/zarr-accumulation/v1.0.rst b/docs/extensions/zarr-accumulation/v1.0.rst index 3d2e990e..17eaec5f 100644 --- a/docs/extensions/zarr-accumulation/v1.0.rst +++ b/docs/extensions/zarr-accumulation/v1.0.rst @@ -13,7 +13,7 @@ Corresponding ZEP: Suggest an edit for this spec: `GitHub editor `_ -This proposal is licensed under the Apache License, Version 2.0. +This proposal is licensed under `the Apache License, Version 2.0 `_. ----