一維顯式時變傾斜雲模式(explicit one-dimensional time-dependent tilting cloud model, ETTM)是由Chen and Sun (2004)所提出的一維雲模式。ETTM模式考慮了雲的傾斜角的存在，所以雲的傾斜軸不必和(r,θ)平面垂直，因此更符合雲內水平對稱的假設。ETTM模式主要是由上衝流和下衝流所組成，兩者皆使用相同動力和熱力方程式。上衝流是由溼熱包做為初始條件，而下衝流則是由降水的蒸發冷卻和拖曳力所形成。 為了檢驗、修正ETTM模式的特徵與模擬結果，在本研究中使用WRF模式，做為三維雲解析模式。因為WRF模式本身具有和ETTM相同的雲微物理(Purdue Lin scheme)，所以利用WRF模擬三維雲的發展，與ETTM模式相比較，並做為未來改進ETTM模式表現的依據。 本研究所選用了兩個觀測實驗探空，分別為RICO和IHOP。其CAPE分別為1397 與2449 。將這兩探空做為初始條件，放入WRF與ETTM模式中模擬。其中ETTM模式在模擬時，所需要上衝流的平均半徑與傾斜角，是從WRF模擬三維雲發展時，在最大垂直速度發生時所求得。 在WRF三維雲解析模式的模擬結果來看，當植入bubble半徑增大時，最大垂直速度也會隨之增強。且上衝流平均半徑與傾斜角，也和bubble有相當的關係。ETTM的模擬結果，在沒有增加低層水氣時，上衝流與雲的強度、高度，並沒有辦法獲得和三維模式相似的結果。而在增加低層水氣場至88%和95%後，上衝流的最大垂直速度強度有明顯的增強，甚至超過三維的平均值。 在比較質量通量、熱通量和水氣通量場上，一維(95%個案)的值都大於三維的值，但是基本上最大值出現的高度是差不多的，主要是因為當水氣增加後，上衝流的強度也隨之增加，所以垂直質量、水氣通量才會較大，但是隨著上衝流平均半徑變大，一維模式的通量高度就不能獲得和三維的高度。所以從兩模式的比較，可知在ETTM模式中，可能對水氣的輻合強度不夠，所以才會造成在沒有增加低層水氣場時，雲發展的強度和三維的結果差很多。 An Explicit one-dimensional Time-dependent Tilting cloud Model (ETTM) developed by Chen and Sun (2004) was adopted for this study. ETTM considers the tilting effect of the cloud. So the tilting axis is not necessarily orthogonal to the horizontal plane (r,θ), making the horizontal axisymmetric assumption more reasonable. ETTM model consists of an updraft and a downdraft. Both are governed by the same dynamic and thermodynamic equations. The updraft is initiated by a moist thermal bubble, while the downdraft is triggered by the evaporative cooling and the drag force of precipitation separating from the tilting updraft. The Weather Research and Forecasting (WRF) model was used as a 3D cloud-resolving model. The Purdue Lin microphysics scheme in the WRF,is the same as that in ETTM.. Therefore, WRF model was used to help identify the characteristics of the ETTM model and to help further improve the performance of the ETTM model. In this study, the input soundings were chosen from two field experiments: IHOP (International H2O Project), and RICO (Rain In Cumulus over the Ocean). The Convective Available Potential Energy (CAPE) is about 1400 for RICO and 2450 for IHOP. Two soundings were used as initial conditions for both WRF and ETTM. The ETTM’s radius and the tilting angle were directly estimated from WRF simulated 3D clouds. Results from WRF showed that the maximum vertical velocity took a longer time to reach when the bubble size increased. In addition, the tilting angle and the average radius also strongly depended on the bubble size. With original soundings, simulated clouds from ETTM were much weaker than those from WRF. After adding moisture (i.e., a moist thermal bubble) into the low levels of ETTM, the results were much reasonable. The mass, heat and moisture fluxes in the vertical direction were calculated and compared between these two models. Results from ETTM with a constraint of at least 95% of relative humidity at low levels were large than those from WRF. However, the heights of the maximum values from both models were comparable and this is critical when the ETTM is used in cumulus parameterization.
