摘要 譜帶劃分(band dividing)是進(jìn)行大氣輻射計(jì)算的基礎(chǔ)，基于各種需要的譜帶結(jié)構(gòu)會(huì)直接影響大氣輻射的精度和速度；本文給出了五種針對(duì)不同需要的譜帶結(jié)構(gòu)，并對(duì)它們對(duì)大氣輻射通量和冷卻率的影響進(jìn)行了詳細(xì)的比較，給出可用于目前氣候模式的帶劃分方案(scheme)。k-分布間隔點(diǎn)(k-interval)的選取是相關(guān)k-分布方法計(jì)算的基礎(chǔ)，如何選取k-分布間隔點(diǎn)是目前大氣輻射計(jì)算中沒(méi)有解決的問(wèn)題之一。本文通過(guò)數(shù)值計(jì)算指出：在其它條件相同的情況下，譜帶劃分和k-分布間隔點(diǎn)的選取是影響大氣輻射計(jì)算精度的兩個(gè)較為重要的因子。如果計(jì)算機(jī)能力允許，增加譜帶和k-分布間隔點(diǎn)的個(gè)數(shù)是提高大氣輻射計(jì)算精度的有效手段。計(jì)算結(jié)果表明，輻射計(jì)算精度對(duì)k-分布間隔點(diǎn)的增加存在飽和度。本文提出了k-分布間隔點(diǎn)選取的優(yōu)化原則和方法，并在此基礎(chǔ)上，給出了可應(yīng)用于氣候模式的多種大氣吸收輻射計(jì)算方案。

Abstract:  Band dividing is the basic of atmospheric radiation calculation, so structure of bands founded on various demands would directly influence the precision and speed of atmospheric radiation. This article lists 5 kinds of bands structure contraposing to different demands, draws a particular comparison among the impact of them on atmospheric radiation flux and cooling rate, and also gives a scheme of band dividing available for the present climate patterns. Selection of k-interval is the foundation of ck-D method, and the problem of how to do the selection still remain unsettled. This article points out through numerical computation that band dividing and selection of k-interval are the major factors influencing the precision of atmospheric radiation calculation, under the circumstances of other conditions be equal. If the ability of computer permitting, to increase bands and number of k-intervals are efficient means for improving the precision of calculation. The outcomes show that there is a kind of saturation of the precision in contrast to the increase of k-intervals. This article puts forward some optimum principles and methods for k-interval choice, and based on it, gives many schemes for calculation of the absorption by gases of radiation applied to climate patterns.
 

      目前，氣候模擬和氣候預(yù)測(cè)成為世界各國(guó)科學(xué)家研究的焦點(diǎn)和難點(diǎn)問(wèn)題。而輻射過(guò)程作為氣候模擬中最為關(guān)鍵控制因子之一，將在很大程度上影響氣候模擬的結(jié)果。長(zhǎng)波輻射在影響天氣、氣候和氣候?qū)ν獠枯椛鋸?qiáng)迫的敏感性上起著關(guān)鍵的作用；太陽(yáng)輻射是地球氣候最終的能量源，在短波輻射加熱率計(jì)算中的一個(gè)小的誤差就可能引起氣候模擬中很大的誤差。隨著模式空間和時(shí)間分辨率的增加和物理過(guò)程的改進(jìn)，氣候模擬對(duì)一個(gè)高精度、高速度的輻射模塊的需求顯得越來(lái)越迫切。

At the present time, climate modeling and climate prediction are the focal points and difficulty with research of scientists all over the world. The process of radiation, being one of the most crucial controlling factor of climate modeling, will affect the result to a large extent. Long wave radiation plays a very important role in influencing weather, climate, and sensitivity of climate to external radiation force. Solar radiation is the foremost source of energy for Earth climate, so a minor error in calculation of the heating rate about short wave radiation may cause a prodigious mistake in climate modeling. Along with advance of space and time resolution and betterment of physical process in the modeling pattern, the need for a high precision, high speed module of radiation grows more and more exigent.
 

      雖然逐線積分方法的計(jì)算精度較高，但由于需要的計(jì)算時(shí)間長(zhǎng)，導(dǎo)致計(jì)算成本大大增加，所以不能直接應(yīng)用在氣候模式中^[1，2]。進(jìn)入20世紀(jì)90年代以后，相關(guān)k-分布方法作為對(duì)逐線積分方法的高精度和低成本近似，已被廣泛用于氣候模擬研究中^[3~11]。但是，即使利用相關(guān)k-分布方法進(jìn)行計(jì)算，也要在精度和速度之間做出選擇^[11]。對(duì)大多數(shù)相關(guān)k-分布方法，對(duì)大氣透過(guò)率的計(jì)算是采用高斯積分或其它數(shù)學(xué)公式積分進(jìn)行的^[7~12]。k-分布間隔（高斯節(jié)點(diǎn)）和k-分布（高斯）權(quán)重的選取對(duì)大氣透過(guò)率的計(jì)算精度有很大影響。關(guān)于如何計(jì)算k-分布間隔點(diǎn)上的吸收系數(shù)，在Zhang et al.(2003)^[11]和Mlawer et al. (1997)^[7]已給出詳細(xì)的研究。到目前為止，k-分布權(quán)重的計(jì)算有三種方法：第一種是采用改進(jìn)的高斯-勒讓德積分間隔來(lái)調(diào)整積分權(quán)重^[7]；第二種是對(duì)原始高斯積分進(jìn)行某種變換，使得能在k-分布曲線變化劇烈的部分選取較多的k-分布間隔點(diǎn)，以來(lái)提高計(jì)算精度^[9~12]；第二種就是通過(guò)SQP（Successive-Quadrature Program）非線性優(yōu)化方法，由迭代法和試錯(cuò)法來(lái)選取k-分布間隔點(diǎn)數(shù)和積分權(quán)重^[8]，但是，該方法容易出現(xiàn)負(fù)權(quán)重和迭代不收斂^[11]。關(guān)于如何選取k-分布間隔點(diǎn)數(shù)的研究較少，除上述SQP非線性優(yōu)化方法外，一般采用固定點(diǎn)法^{[7,9,10,12,13]}，該方法通常在某一計(jì)算譜區(qū)間內(nèi)以選取較多的k-分布間隔點(diǎn)數(shù)，即，增加計(jì)算量，從而降低計(jì)算速度為代價(jià)來(lái)提高計(jì)算精度。實(shí)際上，本文研究發(fā)現(xiàn)，對(duì)某一固定譜區(qū)間，計(jì)算精度對(duì)k-分布間隔點(diǎn)數(shù)的增加存在一定的飽和度，超過(guò)該飽和度，即使再增加點(diǎn)數(shù)，也不會(huì)增加計(jì)算精度。本文將著重討論如何劃分譜帶和選取k-分布間隔點(diǎn)，以及不同譜帶劃分方案、不同k-分布間隔點(diǎn)數(shù)對(duì)大氣輻射通量和冷卻（或加熱）率的影響，并在此基礎(chǔ)上，給出可用于氣候系統(tǒng)模式的多種大氣吸收輻射計(jì)算方案。

Although precision of line-by-line integration(LBL) method is high, it would take a long time to calculate, resulting in the cost increases greatly, so it cannot be immediately used in climate patterns^[1~2]. After the 1990s, the ck-D method has been widely applied in climate modeling research, as it is close to the high accuracy and low cost of LBL method^[3~11]. However, even using ck-D method, there should be a choice between precision and velocity^[11]. For most of ck-D method, atmospheric transmittance is calculated by Gaussian integral or integration of other mathematical formulas^[7~12]. Selection of k-interval(Gaussian node) and its (Gaussian) weight have a strong impact on the precision of atmospheric transmittance. About how to reckon the absorption coefficient on k-intervals, Zhang et al.(2003)^[11] and Mlawer et al. (1997)^[7] have done detailed research. Up to now, there are 3 methods to calculate ck-D weight: the first is using modified Gauss-Lerard integration interval to adjust the weight^[7]; the second is doing certain transform to original Gaussian integral, so as to select more k-intervals where the ck-D curve varies acutely, in order to promote the precision^[9~12]; and the third one is adopting non-linear optimization method of Successive-Quadrature Program(SQP), to choose k-interval and the weight by iterated method and trial-and-error method^[8]. Yet, negative weight or non-convergent iterated results are likely to appear with the third method^[11]. There has been less research on how to decide the number of k-intervals: beside the SQP method, fixed-point method is commonly used^{[7,9,10,12,13]} which usually chooses a lot of k-intervals in a certain band section to increase amount of calculation, so as to improve precision at the expense of reducing efficiency. Actually, the author discovered that a saturation exists with the precision in a fixed band section, when the saturation is exceeded, even though the number of k-intervals increases once more, precision will not improve any longer. This article emphasizes on discussing how to divide the bands and select k-intervals, as well as the influence of different schemes and number of k-intervals on atmospheric radiation flux and cooling(or calefaction) rate, and based on them, gives diversiform schemes for calculation of the absorption by gases of radiation available for climate patterns.
 

 

      由于LBLRTM (Line-By-Line Radiative Transfer Model)^[14~16] 是目前國(guó)際上較為公認(rèn)的逐線積分輻射傳輸模式，本文將采用LBLRTM計(jì)算吸收氣體（包括H₂O，CO₂，O₃，N₂O，CH₄，O₂）的線吸收系數(shù)和H₂O，CO₂，O₃和O₂的連續(xù)吸收系數(shù)。輻射傳輸方法采用張華等（2004）^[2]給出的計(jì)算方案，下面將給予簡(jiǎn)要介紹。對(duì)長(zhǎng)波輻射傳輸?shù)挠?jì)算方法，對(duì)平面平行大氣均勻子層，主要采用Lacis 和 Oinas(1991) ^[6]孤立層熱輻射的思想，并利用改進(jìn)的漫射率因子近似方法^[17]，用作為光學(xué)厚度函數(shù)的漫射率因子來(lái)計(jì)算通量透過(guò)率；對(duì)非均勻大氣，可以用多個(gè)均勻子層來(lái)表示大氣的垂直非均勻性。對(duì)吸收系數(shù)隨壓力和溫度的變化，假定各子層內(nèi)都是均勻的，但具有一種層內(nèi)的溫度梯度，然后用累加法來(lái)計(jì)算各層向上和向下的輻射通量。對(duì)短波輻射傳輸，首先將非均勻大氣分成許多均勻的子層，對(duì)每一個(gè)均勻子層，將求解漫射輻射傳輸矩陣方程問(wèn)題轉(zhuǎn)化為尋找均勻大氣反射率，透過(guò)率和源函數(shù)矩陣的本征值問(wèn)題。首先利用矩陣算子來(lái)表示反射率，透過(guò)率和源函數(shù)^[18]，并采用 二流近似^[19]，將反射率、透過(guò)率和源函數(shù)矩陣轉(zhuǎn)化為標(biāo)量；對(duì)非均勻大氣層采用相加法^[20]。詳細(xì)算法參見(jiàn)文獻(xiàn)^[8]。

Since the LBLRTM(Line-By-Line Radiative Transfer Model)^[14~16] is internationally recognized, it will be adopted in this article to calculate the linear absorption coefficient of absorptive gases(including H₂O, CO₂, O₃, N₂O, CH_4, O₂) and sequential absorption coefficient of H₂O, CO₂, O₃ and O_2. The author will briefly introduce the method of Radiation Transfer put forward by Zhang Hua et al.(2004)^[2]. In the calculation of long wave radiation transfer, for well-proportioned sub-layers of planar parallel aerosphere, permeation ratio of flux is computed by modified approximation-technique of diffusion ratio factor^[17] which is regarded as an optical thickness function, according to the theory about thermal radiation of isolated layer explained by Lacis and Oinas(1991)^[6]. Whereas for asymmetrical atmosphere, vertical asymmetry could be expressed by many symmetrical sub-layers. As for the variation of absorption coefficient along with pressure and temperature, presuming that it is symmetrical within each sub-layer, but there is grads of temperature inside a layer, then accumulate radiation flux of each layer upwards and downwards. When it comes to short wave radiation transfer, primarily dividing the asymmetrical atmosphere into lots of symmetrical sub-layers, thus translating the problem of seeking answer to matrix equation of diffusive radiation transfer into that of seeking reflectivity, permeation ratio of symmetrical atmosphere and latent value of source function matrix. The latter ones are indicated by matrix arithmetic operators^[18], and transformed into scalar quantity by δ–Minor Approximation-technique^[19]; logical addition is applied for asymmetrical aerosphere^[20]. Detailed arithmetic see also Reference[8].