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The Applicability and Modification of Takahashi Formula for Evaporation Estimation in Lhasa
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摘要: 选用1993—1999年拉萨站资料，通过比较多种计算方法得到的潜在蒸散量、高桥浩一郎在1979年提出的基于温度和降水量计算蒸发量的公式所得到的蒸发量以及中日季风试验资料的观测值可知：受温度、水分及相对湿度的影响，潜在蒸散量在5月达到最大值，而蒸发量的最大值则出现在7月。由于青藏高原存在冻土及融冰化雪的特殊现象，水分来源并不完全依靠于降水，所以由高桥浩一郎公式的计算值与观测值之间存在较大差距，温度越高，差值越大；鉴于温度与该差值呈正比关系，可将温度划分为小于0℃，0~5℃，5~10℃，10~15℃，大于15℃共5个等级，在不改变高桥浩一郎公式原有系数的基础上，同时考虑不同的系数对降水量进行修正，修正后的结果明显好于修正前，与观测值更接近。Abstract: Researches on the latent heat, the process of water balance and the dry climate of Tibetan Plateau are of great significance. But due to the limits of estimation methods, observation instruments and lack of stations, there is no long, accurate evaporation data on Tibetan Plateau. Therefore, it is important to choose a more efficient, simple formula to estimate evaporation. The data of the Lhasa can represent the average state of the entire Plateau. In order to calculate the evapotranspiration, several methods including Takahashi formula are adopted and the results are compared with data of the Asian Monsoon Experiment. The result shows that the calculated values are close by PM formula, Remanenko formula, Blaney-Criddle formula and Hargreaves formula. The values calculated by PM formula and Remanenko formula begin to increase from January, reaching the maximum in May, and then decreases. But for the values calculated by Blaney-Criddle formula and Hargreaves formula, the maximum appears in July, two months later. The values of Remanenko formula and PM formula are closest, so the Remanenko formula can be used for the area lack of data. The maximum of potential evapotranspiration appears in May, but the evaporation is smaller due to lack of water, though the sun radiation is strong. As the relative humidity increases with precipitation, the potential evapotranspiration decreases, while the actual evaporation reaches maximum in July. The value estimated by the Takahashi formula has large bias comparing with the observation, indicating that Takahashi formula is not suitable for Lhasa. The bias is greater when the temperature is higher, because the frozen soil, ice and snow thaw on Tibetan Plateau have added the uncertainties. Considering the direct proportion between the temperature and the gapbias, the temperature is divided into 5 grades: Lower than 0℃, 0—5℃, 5—10℃, 10—15℃ and higher than 15℃. Without changing the original coefficients of the Takahashi formula, a coefficient is introduced on the precipitation part, which leads to results closer to the observations. The maximum of actual evaporation appears in summer, reaching 100 mm or above, which is slightly less than the measured value of the Asian Monsoon Experiment, and the minimum appears in winter. The value calculated with the modified formula is significantly higher than the original formula, closer to the observed data. But the value in winter is significantly higher than the original value, slightly higher than the observation.
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Key words:
- Tibetan Plateau;
- evaporation;
- Takahashi formula;
- latent heat
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图 1 不同方法计算的拉萨站1993—1999年潜在蒸散量对比
Fig. 1 The comparison of values calculated by different potential evapotranspiration formulas over Lhasa Station during 1993—1999
图 2 月潜在蒸散量与蒸发量的对比
Fig. 2 The comparison of monthly potential evapotranspiration and evaporation
图 3 高桥公式修正前后计算结果与中日季风试验观测资料的对比及相关分析
Fig. 3 The comparison of results estimated by Takahashi formula before and after correction to observations with correlations among them
表 1 PM方法的潜在蒸散量计算结果与其他方法结果的相关系数对比
Table 1 The comparison of correlation coefficients between values calculated by PM formula and the other formulas
方法 相关系数 Remanenko 0.96 Hargreaves 0.74 Blaney-Criddle 0.64 Linacre 0.63 Kharrufa 0.59 Thornthwaite 0.58 
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表 2 高桥公式修正前后计算的蒸发量与中日季风试验观测资料对比
Table 2 The comparison of results estimated by Takahashi formula before and after correction to observations
月份 观测值/mm 高桥公式修正前 高桥公式修正后 计算结果/mm 相对误差/% 计算结果/mm 相对误差/% 1 3.1 0.7 76.8 7.9 152.0 2 13.4 2.3 82.7 12.2 8.6 3 29.4 5.3 81.8 20.8 29.1 4 19.1 5.4 71.6 24.5 28.1 5 69.9 22.3 68.2 45.4 35.2 6 99.5 55.5 44.3 93.6 6.0 7 130.3 58.9 54.7 102.6 21.3 8 69.6 51.9 25.3 82.9 19.1 9 55.5 49.1 11.6 57.5 3.7 10 26.4 5.4 79.6 23.8 9.5 11 6.3 0.5 91.7 11.9 88.5 12 3.3 0.1 96.5 5.8 77.7
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