基于统计检验的降雨侵蚀力简易计算模型比较

doi:10.18402/resci.2018.08.12

摘要/Abstract

摘要：

降雨侵蚀力因子（R）的准确估算对提高侵蚀预测的精度具有重要作用,但R的计算需要高时间分辨率的降雨过程资料。基于日、月、年降雨资料,目前已开发了众多的R值简易计算模型（PR）。本文通过Meng’s检验比较了不同PR模型结果与R的相关性是否存在显著性差异,并以此为基础评估了国内外15种PR模型在中国东部地区的适用性。结果表明,15种PR模型计算结果与R均显著相关（r >0.59,p<0.03）,表明这些方法均适用于中国东部地区,但由于存在系统偏差,许多模型需要按文中建立的回归关系式校正后得到更优的估算结果。相关系数的统计学比较表明,日降雨PR模型的计算结果与R相关性明显优于年和月降雨模型,而年和月降雨模型差异不明显。所有模型中,3种基于中国数据（包括国内最常用的章文波模型和第一次全国水利普查采用的模型）和1种基于澳大利亚数据建立的日降雨PR模型的相关性并列处于最高等级（r >0.99）,但该澳大利亚模型的计算偏差随纬度增高而变大,章文波模型也存在约30%的系统误差,两者校正后使用能获得更好的效果;第一次全国水利普查采用的模型则可以直接用于R的估算,不需要进行校正处理。论文最终给出了获取不同时间分辨率降雨资料时建议使用的PR模型。

关键词: 土壤侵蚀, 降雨侵蚀力, 相关系数, Meng’s检验, 统计检验, 简易计算模型

Abstract:

The accurate estimation of rainfall erosivity (R) is significant for soil erosion prediction. However, the algorithm for the R factor of the universal soil loss equation (USLE), the most widely used algorithm to calculate R, needs pluviograph data with high temporal resolution. Thus, studies have developed a large number of proxies for the R factor (PR) using daily, monthly, yearly rainfall data instead of pluviograph data. It is noted that the statistical evolutions of the PR_s is desirable, which is currently lacking. This study aimed to evaluate 15 widely used PR_s, including two yearly, six monthly, and seven daily ones, and further rank them in terms of their correlation with R using a stepwise Meng’s test procedure and data collected at 14 rainfall stations in the eastern China. The results indicated that the 15 PR_s under examination were all significantly correlated with R (r > 0.59, p < 0.03), implying all of them can be reasonably used as an R predictor. The stepwise Meng’s test illustrated that the daily PR_s were better correlated with R than the monthly and yearly PR_s with four daily PR_s, which included three developed in China and one developed in Australia, ranking the first (r > 0.99) between the 15 PR_s. Additional examination did show that the Australia PR exhibited a relative error that increased with the latitude and thus should be calibrated by means of the regression equation we developed. One of the three Chinese PR_s did not show a systematic error and can be directly used to estimate R without calibration. The two other PR_s showed approximately 30% overestimation and also be calibrated by the developed regression equations. We also recommended the PR_s to be used if only the monthly or yearly rainfall data is available.

Key words: soil erosion, rainfall erosivity, correlation coefficient, Meng’s test, statistical text, simplified estimating model

马小晴, 郑明国. 基于统计检验的降雨侵蚀力简易计算模型比较[J]. 资源科学, 2018, 40(8): 1622-1633.

Xiaoqing MA, Mingguo ZHENG. Statistical evaluation of proxies for the R factor of the Universal Soil Loss Equation[J]. Resources Science, 2018, 40(8): 1622-1633.

图/表 6

表1

降雨侵蚀力简易计算模型"

	方程	建模地区	参考文献编号	变量说明
年降雨量资料				PR_i表示第i个降雨侵蚀力简易计算方法; AR_i、MR_j和HMR_k （MJ·mm/（hm²·h·a））分别表示第i年,第j月和第k个半月的降雨侵蚀力值; p_j、p_a、p_i、p和MAP（mm）分别表示第j月的降雨量,年降雨量,第i月的年平均降雨量,最高的月平均降雨量以及年平均雨量; rain₁₀（mm）表示一个月中日降雨量超过10mm的月降雨量,day₁₀表示一个月中日降雨量超过10mm的天数; P_d_{>12.7(12, 0)}（mm）表示大于12.7mm（或12mm或0mm）的日降雨量; P_dmax（mm）表示多年平均的最大日降雨量; H（m）和L分别表示站点的高程和以十进制为单位的纬度; S（mm）表示多年平均的雨季降雨量（对于北半球区域为5—9月的降雨量,对于南半球区域为11—4月的降雨量）; α、β、和η表示模型计算的参数,这些参数针对某一固定的站点为常量; F、MFI分别表示Fournier指数和修正的Fournier指数。
	PR₁=0.048 30MAP^1.610 (P<850mm) PR₁=587.8-1.219 MAP+0.004105 MAP² (P ≥ 850mm)	美国	[10]
	PR₂=699.3+7.000 1 MAP-2.719 0H	美国	[11]
月降雨量资料
	$P R 3 = 9.8 × ∑ i = 1 n A R i = ∑ i = 1 n ∑ j = 1 12 1.735 10 1.5 log p j 2 p a - 0.818 8$	美国	[12]
	PR₄=0.073 97 MFI^1.847 (MFI<55mm) PR₄=95.77-6.081MFI+0.477 0MFI² (MFI ≥ 55mm) $MFI = ∑ i = 1 12 p i 2 MAP$	美国	[10]
	PR₅=21.56MFI^0.927	西班牙	[2]
	PR₆=25.1F $F = p 2 MAP$	西班牙	[13]
	PR₇=0.358 9MFI^1.9462	中国	[14]
	$P R 8 = 10 × ∑ j = 1 12 0.012 5 p j 1.6295$	中国	[15]
日降雨量资料
	$P R 9 = ∑ i = 1 n ∑ j = 1 12 M R j = ∑ i = 1 n ∑ j = 1 12 6.97 rai n 10 j - 11.23 da y 10 j$	马来西亚	[16]
	$P R 10 = ∑ i = 1 n ∑ j = 1 12 M ∑ i = 1 n ∑ j = 1 12 0.266 (rai n 10) j 2.071 (da y 10) j - 1.367$	马来西亚	[16]
	$P R 11 = ∑ i = 1 n ∑ k = 1 24 HMR k = ∑ a = 1 n ∑ k = 1 24 α ∑ m = 1 n P d ≥ 12 m β$ $α = 21.586 β - 7.1891$ $β = 0.836 3 + 18.144 P d 12 + 24.455 P y 12$	中国	[17]
	$P R 12 = ∑ i = 1 n ∑ k = 1 24 HMR k = ∑ a = 1 n ∑ k = 1 24 α ∑ m = 1 n P d ≥ 12 m β$ $α = 10 2.124 - 1.495 β + 0.00 214 P d max$ $β = 0.836 3 + 18.144 P d 12 + 24.455 P y 12$	中国	[18]
	$P R 13 = ∑ i = 1 n ∑ k = 1 24 HMR k = ∑ a = 1 n ∑ k = 1 24 α ∑ m = 1 n P d ≥ 12 m 1.726 5$ $α = 0.393 7 暖季 (5 — 9 月) 0.310 1 冷季 (10 — 12 月, 1 — 4 月)$	中国	[19]
	$P R 14 = ∑ i = 1 n ∑ j = 1 12 M R j = ∑ i = 1 n ∑ j = 1 12 α 1 + η cos 2 π fi - ω ∑ m = 1 n P d ≥ 12.7 m β$ $f = 112; ω = π 6; β = 1.49; η = 0.29 α = 0.359 1 + 0.098 9 exp 3.26 S / MAP$	澳大利亚	[20]
	$P R 15 = ∑ i = 1 n ∑ j = 1 12 M R j = ∑ i = 1 n ∑ j = 1 12 α 1 + η cos 2 π fi - ω ∑ m = 1 n P d ≥ 0 m β$ $f = 112; ω = π 6; η = 0.3 β = 1.02 - 0.020 9 L α 0 = 1.05 × 10 2.08 - 1.58 β α / α 0 = 2.349 + 0.040 40 L - 0.000 268 4 H$	澳大利亚	[21]

表1

表2

图1

表3

图2

图3

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省份	名称	经度/°E	纬度/°N	高程/m	降雨资料年数/a	R/(MJ·mm/（hm²·h·a）)
黑龙江	嫩江	125.13	49.10	222.3	30	1 368.7
黑龙江	通河	128.44	45.58	108.6	38	1 632.5
山西	五寨	111.49	38.55	1 401.0	30	781.9
山西	阳城	112.24	35.29	659.5	30	1 503.3
陕西	绥德	110.13	37.30	929.7	29	992.8
陕西	延安	109.30	36.36	958.5	39	1 233.7
四川	西昌	102.16	27.53	1 590.9	40	3 021.0
四川	遂宁	105.35	30.30	278.2	33	4 091.3
湖北	房县	110.46	32.02	426.9	31	2 298.4
湖北	黄石	115.03	30.15	19.6	32	6 049.4
云南	腾冲	98.30	25.01	1 654.6	36	3 648.9
云南	昆明	102.41	25.01	1 892.4	33	3 479.0
福建	福州	119.17	26.05	84.0	39	5 871.1
福建	长汀	116.22	25.51	310.0	31	8 258.5

PRi	直接估算			修正后估算
	MRE	RMSE	NSE	MRE	RMSE	NSE
	/%	/（MJ·mm/（hm²·h·a））		/%	/（MJ·mm/（hm²·h·a））
PR₁	29.0	1 287	0.65	31.8	1 183	0.70
PR₂	174.3	4 122	-2.60	15.9	775	0.87
PR₃	32.5	1 459	0.55	29.9	1 102	0.74
PR₄	147.0	5 819	-6.18	32.7	1 262	0.66
PR₅	31.0	2 128	0.04	26.6	1 195	0.70
PR₆	57.5	2 978	-0.88	54.9	1 755	0.35
PR₇	58.8	2 438	-0.26	31.7	1 253	0.67
PR₈	17.7	895	0.83	15.2	816	0.86
PR₉	96.8	2 396	-0.22	13.1	703	0.90
PR₁₀	29.2	1 457	0.55	12.9	454	0.96
PR₁₁	31.7	1 314	0.63	10.6	316	0.98
PR₁₂	35.5	1 550	0.49	11.0	299	0.98
PR₁₃	12.5	376	0.97	9.7	351	0.97
PR₁₄	49.9	1 294	0.65	18.7	1 103	0.74
PR₁₅	28.2	698	0.90	14.1	361	0.97
均值	55.4	2 014	-0.26	21.9	862	0.80