ICESat-2 ATLAS大气延迟校正算法理论基础文档

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本篇文档是关于ICESat-2项目的ATBD（Algorithm Theoretical Basis Document，算法理论基础文档）的一部分，标题为"ICESat2_ATL03A_ATBD.pdf"。该文档详细介绍了由Goddard Space Flight Center在Maryland的Greenbelt地区为ICESat-2任务开发的高级地形激光高度计系统（ATLAS）产品的数据处理算法和理论依据。ATLAS仪器包含了科学算法软件(ASAS)和调度及数据管理系统(SDMS)，它们共同协作以生成从原始观测数据到0到4级的标准数据产品。 0级数据是未经处理的基础数据，而后续的1至4级数据则是经过大气延迟校正、辐射校正、轨道和姿态纠正等多个步骤处理后的产物，包括激光测高范围数据、地形信息和质量评估。其中，大气延迟校正是关键环节，因为地球大气对激光信号传播的影响需要精确计算和去除，以得到地面的真实高度。文档特别强调了所有处理过程都是在ICESat-2科学研究者的指导下，在SIPS（ICESat-2 Processing System）上进行的，这个系统确保了数据的准确性和一致性。此外，对于任何修改或更新，都必须经过科学发展团队的批准，并通过ICESat-2 Management Information System (MIS) 的Signature Control Request (SCoRe) 进行提交，以确保变更的合理性和文档的权威性。文档的作者L.Petrov，代码为698，提供了联系信息，以便用户在使用前验证文档版本的正确性。最后，文档中的指令清晰明了，使用了诸如"shall"、"should"、"may"和"can"等词来指示不同的行为准则和建议，使得读者能够明确理解其在项目中的角色和责任。本篇文档对于理解ICESat-2项目中大气延迟校正在激光测高数据获取中的重要性，以及数据处理流程和规范具有重要参考价值，对于科学家、工程师以及对地球表面观测感兴趣的各方来说，都是不可或缺的技术指南。

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bottom edge of the kth layer and P

(k) is the atmospheric at the top of the kth layer. Air temper-

ature and speciﬁc humidity are provided for the middle of the layer. The upper edge of the highest

pressure level is ﬁxed: 1Pa. Atmospheric pressure at a given layer can by produced by summing

the pressure at the layers from the top (See Figure 3.1.2).

The right hand-side of expression under integral 8 is not known at the surface, which corresponds

to the bottom edge of the lowest layer. it can be computed by linear extrapolation:

(s) =

(l) + ∆P (l)/2

(l − 1) −

(l)

P (l − 1) − P (l)

P (s) = P (l) + ∆P (l)/2

(9)

where l is the index of the lowest layer. Remember, for GEOS-FPIT the lowest layer has the

greatest index. We extend

and P to the surface: P (0) and

(0) and use these extended

functions for further analysis.

In order to compute integral 8, we expand the expression under the integral into B-spline basis

of the 3rd degree: f(P) =

n−1

1−m

(P ), where B

(P ) is the B-spline function of the m-th degree

with the ith pivotal element with n + 1 nodes that are indexed starting from 0. Then

h(P

) = h

k−1

i=1−m

(P ), (10)

where I

(x) =

∞

(x) dx — a function that is expressed via B-splines of m + 1 degree. If to

introduce function L

i,k

(x) = I

)−I

k−1

) =

k−1

(x) dx and keeping in mind that B

(x)

is zero outside interval [x

k−m

, x

k+1

], expression 10 can be re-written as

h(P

) = h

(11)

h(P

) = h(P

k−1

) +

k−1

i=k−m−1

i,k

(P ). (12)

where index 0 corresponds to the surface and index k > 0 corresponds to the middle of a layer.

Then at each element of the grid we compute g(h(P

)) using expression 5 and make the second

iteration. As a result, we obtain height above the reference ellipsoid for each layer of total pres-

sure, air temperature and speciﬁc humidity q. Finally, we transform speciﬁc humidity into partial

pressure of water vapor:

1 −

P. (13)

3.1.3. Regridding the state of the atmosphere to the regular grid

The grid of parameters P , P

, and T is irregular: the grid step along level axis depends on

latitude, longitude and time. Interpolation at a multidimensional irregular grid is impractical. The

Release date TBD 7

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next step of the data processing chain is to re-cast the atmosphere state parameters to a new

regular grid that has ﬁxed height of levels. It should be noted that for eﬃcient interpolation the

new grid does not need to be uniform, i.e. to have a constant step. Since at the ﬁrst approximation,

atmospheric pressure varies linearly with P , a grid with a uniform step over log(P ) will introduce

less artifacts than a grid with a uniform step over P.

The following grid is suggested:

= exp

i − µ

− µ

(14)

where µ

= 20.25319, µ

= 1200.0, µ

= −169.30782 for i ∈ [−62, 62]. The grid runs from -1000 to

90,000 meters above the reference ellipsoid. The new grid is wider and has 55% more nodes. Such

a grid was selected to have density of nodes no less than the initial grid in order to avoid loss of

accuracy during regridding.

The nodes of the uniform grid fall into three regions: 1) the region below the assumed surface,

2) the region within the range of height of the numerical weather model, 3) and the region above

the modeled top of the atmosphere. Regions 1 and 3 require extrapolation and region 2 requires

interpolation.

We expand total atmospheric pressure, partial pressure of water vapor, and air temperature over

the B-spline basis against height variable. For points in region 2 we use the expansion coeﬃcients

for computing these quantities at nodes of the new uniform grid.

We assume the atmosphere above the highest grid level is isothermal and dry. The extrapolation

is done this way:

P (h

) = P (h

) exp{ −g

− h

R T

}

T (h

) = T

) = 0

(15)

where h

, T

, and g

are height, air temperature and gravity acceleration at the upper pressure

level of the output of the numerical weather model.

We assume the atmosphere obey the adiabatic law with a constant temperature derivatives

∂T

∂h

(so-called lapse rate with the opposite sign) below the ﬁrst pressure level. The lapse rate

near the surface may diﬀer signiﬁcantly from the lapse rate in the middle of the troposphere. For

extrapolation of the state of the atmosphere we prefer to use the representative lapse rate for the

middle of the troposphere. We compute derivative

∂T

∂h

with least squares over the range of heights

from 1000 meters above the ﬁrst level and 9000 meters. Then we compute air temperature and

total pressure at the levels of the new grid as

T (h

) = T (h

) +

∂T

∂h

− h

)

) = P

) (T (h

)/T (h

))

−g(h

) M

/(R

∂T

∂h

)

P (h

) = P

) + (P − P

)(h

) (T (h

)/T (h

))

−g(h

) M

/(R

∂T

∂h

)

(16)

where h

is the height of the ﬁrst level of the output of the numerical weather model.

Of course, accuracy of extrapolation beneath the surface is lower than the accuracy of the

atmosphere state parameters within the range of heights of numerical weather models. We compute

Release date TBD 9

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