GUT手册：欧洲GOCE重力卫星数据处理与海洋学工具

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GUT(Gravity User Toolbox)是欧洲航天局(ESA)为支持Gravity and Ocean Circulation Experiment (GOCE)卫星任务而开发的用户工具包。GOCE卫星旨在提供前所未有的地球重力和大地水准测量精度，这对于海洋环流模型的改进具有重要意义。GUT是一款全面的工具集，专为海洋学和大地测量学研究设计，它方便用户处理GOCE的Level-2数据产品和其他相关数据。 GUT User Guide and Algorithm Descriptions文档详细介绍了GUT的安装、使用和高级功能。该版本为2.0，发布日期为2011年3月9日，共112页。文档内容分为多个部分： 1. **简介**： - 提供了GUT的整体概述，解释其在GOCE项目中的角色以及它如何协助科学家们分析和利用卫星数据。 - 描述了GUT的应用范围，强调其对海洋学和地球物理学研究的实用性。 2. **安装**： - GUT支持多种操作系统，包括Linux、macOS X和Windows。 - 安装方法包括使用预编译的二进制包和从源代码编译，每种方法都提供了详细步骤。 3. **使用GUT**： - 初级用户指南：如何开始使用GUT，包括基本操作、获取帮助、查看版本信息以及执行工作流程。 - 进阶功能：解释了GUT的工作流程执行机制，以及如何创建和检查输入数据、理解工作流程的有向无环图(DAG)结构。 - 用户环境变量管理：确保正确配置环境以优化工具性能。 4. **Spherical Harmonics**： - 详细介绍了与GUT相关的球面谐波基础函数，这是处理地球重力场数据的关键数学工具。 - 包括球面谐波的递归关系，这些关系对于解析和处理地球形状和引力场变化至关重要。 5. **开发新处理单元**：对于高级用户或开发者，这部分内容涵盖了如何创建和定制新的处理单元，以适应特定的研究需求。通过GUT，用户能够充分利用GOCE卫星数据，提升海洋环流模型的精确度，进而推动地球科学领域的前沿研究。该手册为用户提供了全面的操作指南和理论支持，使他们能够高效地进行数据处理和分析工作。

GUT

User Guide and Algorithm Descriptions

Reference : ESA-GUT-AD-001

Version : 2.0 page

Date : 09 Mar 2011 16/112

connected to more than one input.

3.2.3 Command-line input

A work-flow defines the data-flow within a processing chain, but in general it

does not define the data that is to be processed. To facilitate providing data to

(and exporting data from) the work-flow, GUT has a specific group of

processing units. These units can extract information from the gut command-

line and publish that information as an output. They also provide a mechanism

for specifying a default value, in case the user did not provide the required

command-line information. These units, which has type names beginning with

CmdLineArg, are used in the work-flow assembly just like all other types of

units. For tracing and debugging purposes, GUT will also store the complete

command line in the output file.

3.2.4 Structural Verification

The GUT command-line tool will check that all of the restrictions imposed on

the work-flow are satisfied, but passing these checks does not guarantee that

the resultant process chain is what the work-flow designer intended. The

syntax of the work-flow files is simple, but it does not readily convey the graph

structure. The dot run-mode aids development and documentation of work-

flows by exporting a work-flow file in a format that can be used by the GraphViz

software (an open source project). This run mode can be applied to any work-

flow file and is usable on incomplete or incorrectly structured work-flows. In

this run-mode gut will report errors and export to the dot file as much

information as it can.

% gut –-dot geoidheight_gf

The dot file is created in the current directory with a filename that is the work-

flow name with the “.dot” extension. The

dot

and

dotty

tools from the GraphViz

package will permit visualization of the graph. The image generated by the dot

tool from the output of the command above is shown in figure 1.

GUT

User Guide and Algorithm Descriptions

Reference : ESA-GUT-AD-001

Version : 2.0 page

Date : 09 Mar 2011 18/112

temporary files are removed before gut exits, but terminating the

program with a signal (ie. Ctrl-C) may result in temporary files residing on

the system.

● GUT_MEMSIZE_KB : This variable, if set, should be an integer (in

kBytes) specifying the maximum size of a gridded data file that gut will

attempt to manage in system memory. For data size above this limit gut

will create a temporary file for storage and swap data between memory

and file as needed. This allows gut to process files larger than physical

memory but it incurs a performance penalty. The default maximum size

is approximately 65536 kB (64Mb). You should set this to a smaller value

if your system has limited memory and gut fails to allocate memory for

large gridded data sets. You should set the variable to a larger value if

your system has adequate memory and gut is found to be swapping

to/from disk when processing.

(NOTE: the default limit is approximately

equivalent to an equiangular 6'x6' global grid)

3.4 Developing new Processing Units

The processing capabilities of GUT are encapsulated in the suite of processing

units that are an integral part of the command-line tool. Each of these

processing units is defined in a single C++ class and users can extend the GUT

feature set by developing software implementations for new processing units.

Further discussion of this topic is deferred to §10.

4 Spherical Harmonics

A considerable fraction of the GUT data types and algorithms are described and

implemented in terms of arithmetic series of spherical harmonic basis

functions. The foundation of spherical harmonic functions are the Associated

Legendre Functions, and these functions are well described in many texts. In

the field of Geodesy a particular normalization scheme is adopted for these

functions and the resulting spherical harmonic basis functions. This scheme is

also well described in many texts and the GUT software simply follows this

defacto-standard. A brief summary of the relevant equations is provided here

merely for consistency.

4.1 General Spherical Harmonics Basis Functions

The spherical harmonic function of degree

, order

, is given by

GUT

User Guide and Algorithm Descriptions

Reference : ESA-GUT-AD-001

Version : 2.0 page

Date : 09 Mar 2011 19/112



 =

i m



cos

where

(x)

is an Associated Legendre Function, and

a (complex)

normalization coefficient. Note, the notation

(x)

is also used for these

functions, often to avoid confusing the order,

, for a power. In this document

both notations are used.

When spherical harmonics are considered as solutions to Laplace's equation

and boundary conditions are considered, only integral values of

and

are

relevant, with the additional constraint that

|m| < n

The spherical harmonic functions are orthogonal and therefore form a set of

basis functions on the sphere. Consequently, an arbitrary function on the

sphere can be represented as a linear combination of these basis functions.



=

∑

max

∑

=−





The identity,

−



 = −1



−













allows the terms

(,)

and

-m

(,)

to be summed together and then a ℜeal

function can be expressed in terms of weighted sine and cosine functions with

ℜeal coefficients and a single

Associated Legendre Function

. This forms a new

basis set of functions such that the expansion of function

f(,)

is now



 =

∑

max

∑

[

cos



sin

]

cos

In many disciplines the equation above is normalized. This is a simple

transformation to a different set of basis functions, each of which is a scalar

multiple of the functions above. Different normalization schemes are applied in

different disciplines, based largely on the nature of the functions that are

studied. In geodesy the normalization scheme is a simple transformation based

on the degree and order. In many texts the normalized coefficients and

functions are represented with an over-bar. In this text however, the non-

normalized basis functions are only relevant in this summary section, as all

algorithms in GUT are implemented in terms of normalized functions. For this

reason the

over-bars are shown in this section only and omitted in all other

sections

The relationship between normalized and non-normalized functions are

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