_{s}-VI Triangle Method in Terrestrial Evapotranspiration Estimation

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This study aims to investigate the impact of the spatial size of the study domain on the performance of the triangle method using progressively smaller domains and Moderate Resolution Imaging Spectroradiometer (MODIS) observations in the Heihe River basin located in the arid region of northwestern China. Data from 10 clear-sky days during the growing season from April to September 2009 were used. Results show that different dry/wet edges in the surface temperature-vegetation index space directly led to the deviation of evapotranspiration (ET) estimates due to the variation of the spatial domain size. The slope and the intercept of the limiting edges are dependent on the range and the maximum of surface temperature over the spatial domain. The difference of the limiting edges between different domain sizes has little impact on the spatial pattern of ET estimates, with the Pearson correlation coefficient ranging from 0.94 to 1.0 for the 10 pairs of ET estimates at different domain scales. However, it has a larger impact on the degree of discrepancies in ET estimates between different domain sizes, with the maximum of 66 W·m^{−2}. The largest deviation of ET estimates between different domain sizes was found at the beginning of the growing season.

_{s}-VI space

Evapotranspiration (ET) from the land surface is an important component in the surface energy balance and water balance. Accurate characterization of it is therefore very important in the study of the terrestrial ecosystem, climate dynamics and hydrologic cycle. At present, estimate of regional evapotranspiration has been made possible by using the remote sensing observations in combination with ancillary surface and atmospheric data. Since the 1980s, a number of satellite-based land surface flux models were developed to simulate surface-atmosphere interactions and to retrieve the terrestrial evapotranspiration over a wide range of spatial scales [_{s}) under a full range of vegetation cover and soil moisture availability within the study region. This model needs fewer assumptions and reduces the complexity of ET estimation over large heterogeneous areas [

A significant number of publications have demonstrated the reliability of this method in estimating regional ET [_{s}-VI triangle space [_{s}-VI space, pixels on which are taken as surfaces with the largest water stress for a range of VI. In contrast, the wet edge is the lower envelope of the T_{s}-VI space, pixels on which represent surfaces without water stress. _{s}-VI space. _{max,i} and _{min,i} are the corresponding maximum and minimum surface temperatures at the dry and wet edges, respectively for a given VI (see

The determination of the dry edge and the wet edge is a critical procedure in the triangle method in that they provide important boundary conditions of the contextual T_{s}-VI relationship. Based on the boundary conditions, EF for a pixel at a specific VI interval is deduced by weighting the extreme T_{s} values within the interval in terms of the T_{s} of the pixel (see Section 2). Therefore, the dry edge and wet edge determine EF for pixels within the two limiting edges and subsequently determine ET estimation.

Normally, the dry edge of the triangle method is derived from the remotely sensed T_{s}-VI scatter plot by a linear fit to data pairs of the maximum T_{s} values at each VI class interval (e.g., [_{s} of the cold pixel with the largest VI value, the T_{s} of a water body or a well-irrigated agricultural field [

In addition, the triangle method assumes uniform atmospheric forcing within the study area. Meteorological forcing is also an important factor influencing surface temperature, as a result affects the determination of the dry/wet edge of the T_{s}-VI space. However, whether the assumption is met is rarely mentioned in literatures when the triangle method is applied. The great difficulty in retrieving regional and accurate data of air temperature may be a major reason for this.

In practice, satellite images with varying spatial coverage can be used to retrieve surface heat flux in the domain of interest. One would use a subset of an image specifically for a study site, taking the entire scene of the image, or even merge multiple scenes of images. Different images used in the calculation would result in different surface heat flux estimates because the corresponding geomorphological features may be different. Usually, increasing the domain size would increase the heterogeneity in the land surface and meteorological conditions, and result in variations in the boundary condition of the triangle method, consequently, influence ET estimates. Therefore, performance of the triangle method depends on the size of the domain being used. Additionally, the impact of spatial extent on the performance of the triangle method also depends on the methodology for estimating temperature endmembers.

The relationship between the domain size and the performance of the triangle method has been studied insufficiently. Chen [_{s} and VI. Long ^{−2} in the sensible heat flux (H) estimates between different domain sizes. They concluded that the variation of surface temperature for the selected extremes (hot pixel and cold pixel) at different domain scales is a major reason for this. Long

The objective of this study is to investigate the dependence of the T_{s}-VI triangle method on the domain size specifically for arid area. By applying the triangle method to five nested subareas of the Heihe River Basin in the arid northwestern China, five sets of ET estimates and the related evaluation matrix are compared. The new findings of this study would be helpful to optimize the size of domain when applying and improving the triangle method.

The triangle method for ET estimation is based on the physical relationship between _{s} and VI or vegetation fraction cover (_{r}) [

The mathematical expression of latent heat flux (LE) is taken as follows (Jiang and Islam 1999):
_{n} is the surface net radiation (W·m^{−2}). ^{−2}). Δ is the slope of saturated vapor pressure at the air temperature (KPa·C^{−1}). γ is the psychrometric constant (KPa·C^{−1}).

The value of _{r} (0 < _{r} < 1). Assuming _{min} = 0 for the driest bare soil pixel and _{max} = 1.26 for the wet edge with the maximum _{r}, global minimum and maximum _{max,i} for each _{r} is very close to 1.26. Given these two bounds, the value of _{r} along the dry edge is used as the lower bound of _{min,i}. The _{i} for any pixel with a _{r} and a surface temperature T_{s}, can be determined by
_{max,i} and _{min,i} are the corresponding maximum and minimum surface temperatures at the dry and wet edges, respectively for a given _{r} (see

In this study, _{n} and _{ld} is the downward longwave radiation and is estimated by the method proposed by Idso and Jackson [_{a} is the air temperature, _{0} is the solar shortwave radiation, _{s} is the surface temperature, _{s}, _{v}) according to their proportion in a pixel (_{s} = 0.96 and _{v} = 0.98 are used in the calculation. _{r} is estimated from the normalized difference vegetation index (NDVI) [

An automatic edge determination algorithm presented by Tang _{s} value at dense vegetation cover was selected as the constant temperature at the wet edge. If pixels show relatively low T_{s} values but not high NDVI values, it implies an absence of dense vegetation cover, generally occurring in the early stage of crop growing season. In this case, quality control data from the land surface temperature product of MODIS was used to exclude pixels that have uncertainties of 3 k in T_{s} retrievals. Then, the pixel with the lowest T_{s} value was taken as the temperature at the wet edge.

Our study area is the Heihe River Basin in the arid northwestern China, ranging in latitude between 37.75°N and 42.67°N and in longitude between 96.07°E and 102.07°E (^{2}, rising in the Qilian Mountain and flowing northward through 11 counties in 3 Provinces to become the East and the West of Juyan Lakes.

The basin comprises three major geomorphologic divisions from the south to the north, namely, the southern Qilian Mountains (the upper reach), the middle Hexi Corridor (the middle reach) and the northern Alxa High-plain (the lower reach). Elevations decrease from the south to the north, ranging from around 5,100 m to 500 m (

To investigate the relationship between the domain size and the triangle model performance, five different spatial domains were set up. The five domains include the entire basin (Domain I in

Data of the daytime surface temperature (LST_Day_1 km), the overpass-time (Day_view_time), 16-day Normalized Difference Vegetation Index (1_km_16_days_NDVI) and 8-day Albedo (Albedo_BSA_Band_shortwave) extracted respectively from the MODIS products of land surface temperature (MOD11A1), 16-day Vegetation Indices (MOD13A2) and 8-day Albedo (MCD43B3) were used as the inputs for the triangle method. All the data were georeferenced and were re-sampled to 1 km spatial resolution with the MODIS Reprojection Tool (MRT). Because T_{s}-VI triangle space can not be constructed during non-growing seasons when there is almost no green vegetation in the basin except the needle-leaved evergreen forest in Qilian Mountains, only the clear-sky MODIS data in 2009 during the growing season from April to September were used. Because only one image is available every 16 days for MODIS NDVI product, data of surface temperature and Albedo matching closest with the date of the NDVI data were used to estimate ET. MOD11A1 quality information was used to exclude MODIS data having large uncertainties in surface temperature retrievals. After screening, days in which valid data can cover 90% of the whole Heihe Revier Basin were kept. Finally, 10 clear-sky days during the growing season from April to September in 2009 were used to investigate the impact of the spatial domain size on the performance of the Ts-VI triangle method in terrestrial evapotranspiration estimation.

As shown in _{0}) and air temperature (_{a}) are required to calculate _{n} and Δ. In this study, meteorological data of _{0} and _{a} from the Global Data Assimilation System (GDAS); the global meteorological weather forecast model of the National Centers for Environmental Prediction [_{0} and _{a} to a 1 km resolution, which uses 4 neighboring points to compute the interpolation weights. A linear interpolation method was used to get _{0} and _{a} at overpass time of MODIS (about 03 UTC at the Heihe River Basin), which computes the temporal weights based on data at 00 and 06 UTC.

Based on the T_{s} and _{r} images covering Domain I, II, III, IV and V, respectively, we obtained five sets of dry/wet edges for each of the 10 days. _{s}_max) over each area for each day.

In general, a slight difference of the intercepts of dry edge for Domain I, II and III was found. Compared with the intercepts for Domain IV and V, Domain I, II and III have much higher values. This phenomenon can be related to _{s}_max corresponding to the five areas. _{s}_max for the five areas for the 10 days. It displays a very good correlation coefficient (R^{2}), indicating high surface temperature of bare soil usually could lead to high intercepts of the dry edge. _{s}_max are the highest for Domain I and II, followed in turn by Domain III, IV and V. As mentioned in Section 3.1, Gobi desert in Ejina and Jinta is the driest surface in the basin and therefore produced the highest _{s}_max for Domain I and II. Comparatively, the absence of extremely dry surface in Domain V results in the lowest intercept of the dry edge.

In addition, it can be seen from _{r} happens much faster for Domain I, II and III. As mentioned in Section 2, the slope of the dry edge is determined by a linear regression between the maximum surface temperatures and the corresponding _{r} interval. In the case where there is a wide range of maximum surface temperature for a range of _{r} resulting from the combined effect of soil moisture, elevation, land use type, a steep slope of the dry edge would be produced. Generally speaking, the larger the domain size is, the more heterogeneous land surface is and thereby the steeper the slope of the dry edge is. The difference between _{s}_max and the minimum surface temperature (c in

The largest differences in slopes of the five domains were observed on DOY (day of year) 96, and 112. It is up to 27.5 K, 22.7 K between Domain I and V, respectively for the two days. The growing season of the dominant crops (maize and spring wheat) in the basin is from April to September. DOY 96 and 112 are at the early stage of the growing season. An absence of densely vegetated surfaces in Domain IV and V during the early stage of the crop growing season leads to a higher temperature for wet surfaces (see c value in _{s} on DOY 96 and 112, and therefore produces the gentler slopes. Values of (a–c) for Domain V for the two days are only 6.3 K and 7.6 K, while values of (a–c) are more than 20 K for the days in the middle of the growing season. The results indicate that the slope of the dry edge in T_{s}-VI space would be obviously overestimated during the early stage of crop growth or for the domain with no full vegetation cover. For Domain I, II and III, low surface temperatures of forest and grass land at high altitudes (

Similar to the largest difference of the slopes for the upper boundaries, the largest contrast in the lower boundaries were also observed between Domain I and V. On DOY 96 and 112, the differences of c values between Domain I and V are as large as 15∼20 K. This is consistent with the above description of the absence of extremely wet surface for Domain V at the beginning of the growing season.

ET estimates from the triangle method is substantially dependent on the boundaries in the T_{s}-VI space via the _{max,i} and _{min,i} using

^{−2} for the 10 days. The largest differences were found between Domain I and V, yielding an RMSD of 29 W·m^{−2} for the 10-day average. This is consistent with the smallest difference in the limiting edges between Domain IV and V and the largest difference between Domain I and V (^{−2}. This can be explained by the larger difference of the dry/wet edges for the domains in the early stage of growing season and the smaller difference in the middle stage of growing season.

For the ET estimates in Domain IV (^{−2}. Similar to the comparison of ET estimates for Domain V, the RMSD of ET estimates between Domain IV and the other three Domain I, II, III are also significantly higher at the beginning of growing season than in the middle, which is as high as 55 W·m^{−2} on DOY 96.

When comparing the ET estimates for Domain II and III (

The trend of ET estimates with increasing domain size was not completely reflected from the mean difference of ET estimates between the five domain sizes. Some days exhibit positive values, while some days exhibit negative values.

The above results indicate that the difference of the dry/wet edges in the T_{s}-VI space may be a key contributor to the difference of ET estimates for domains with different sizes. _{s}-VI space. Apparently, differences in the slopes of the dry edges of the T_{s}-VI space (difference of b value in

Additionally, the average Pearson correlation coefficients

_{s}-VI space with domain size does not influence the spatial pattern of ET estimates. However, there are large differences in the magnitude of ET estimates between different domain sizes in terms of their histograms. Results explicitly revealed that ET estimates from Domain IV, V are much larger than that from Domain I, II and III on DOY 96, showing the areal mean of ET estimates of 72 W·m^{−2}, 76 W·m^{−2}, 32 W·m^{−2}, 33 W·m^{−2} and 32 W·m^{−2}, respectively for Domain IV, V, I, II and III.

To investigate how domain size influences the performance of the triangle method, the method was applied to five nested subareas of the Heihe River basin in arid northwestern China where large variations of land cover, vegetation fractional cover, surface temperature and altitude are found between the five subareas. The impact of spatial extent on the performance of the triangle method resulting from the variability of soil moisture and vegetation cover at the sensor resolution was specially discussed. By comparing the determined dry/wet edges and ET retrievals between the five subareas, the relationship between the triangle method and the domain size is quantitatively investigated.

Results show that: (1) the intercept of the dry edge in the T_{s}-VI space is determined largely by the highest surface temperature in the spatial domain. In the case that the extremely dry surface is absent in the spatial domain, the intercept of the dry edge would be underestimated. In the study, it was underestimated by 20 K on DOY 231. As the domain size is increased, the extreme high surface temperature tends to increase and the extreme low surface temperature tends to decrease. (2) a large range of surface temperature in the spatial domain could lead to a steep slope of the determined dry edge. With the increase of the domain size, the slope of the dry edge tends to be steeper because of the increasing diversity of land surface types. When the extremely dry and wet surfaces are absent, the slope of the dry edge tends to be gentler. The maximum difference of the slopes of the dry edges between different domain sizes is up to 27 in the study. (3) large differences of the limiting edges between different domain size tend to arise in the beginning of the growing season. Because densely vegetated surfaces with low surface temperature are often absent during that time, the range of surface temperature is greatly reduced at a small domain, producing gentler slopes of the dry edge. (4) ET estimates from the triangle method depend on the domain size owing to the domain dependence of the limiting edges of the T_{s}-VI space. The degree of discrepancies in ET estimates between different domain sizes corresponds to the degree of discrepancies in the limiting edges between different domain sizes. The maximum difference of ET estimates of 66 W·m^{−2} between different domain sizes was produced in the study. (5) the Pearson correlation coefficients for ET estimates at different domain scales are as high as 0.99. This indicates that the difference of the determined limiting edges between different domain sizes has little impact on the spatial pattern of ET estimates.

This work was supported jointly by the National Basic Research Program of China (2009CB421305 and 2010CB428403), the National Natural Science Foundation of China (41271380 and 41171286) and the Hundred Talents Program of the Chinese Academy of Sciences (CAS).

The conceptual T_{s}-VI space.

DEM (Digital Elevation Model) map and the administrative division of the Heihe River Basin.

Land cover maps of the five domains in Heihe River Basin (

(

Comparisons of RMSD in ET estimates of Domain IV and Domain V between different domain scales and the difference of the boundary conditions of the T_{s}-VI space (

Distribution maps of ET estimates of domain V calculated from images covering domain I, II, III, IV and V on DOY 96.

Statistics of the determined dry/wet edges, the maximum surface temperature (_{s}_max) over the subarea for 10 clear-sky days.

96 | 315.9 | 316.0 | 315.7 | 311.1 | 310.9 | −32.7 | −32.5 | −31.8 | −5.6 | −5.2 |

112 | 322.1 | 321.9 | 321.3 | 315.9 | 313.7 | −30.4 | −31.2 | −28.8 | −9.9 | −7.7 |

121 | 323.0 | 320.1 | 320.2 | 315.8 | 310.8 | −25.6 | −20.6 | −20.7 | −18.6 | −13.0 |

144 | 327.3 | 327.5 | 326.5 | 325.7 | 322.4 | −25.7 | −26.4 | −24.2 | −21.7 | −18.4 |

152 | 331.3 | 331.3 | 330.9 | 328.2 | 320.1 | −33.9 | −33.9 | −33.6 | −29.1 | −17.7 |

163 | 331.4 | 331.5 | 329.3 | 327.8 | 322.5 | −30.2 | −30.8 | −27.4 | −22.0 | −16.8 |

176 | 332.9 | 333.1 | 331.6 | 330.8 | 328.2 | −26.1 | −26.7 | −24.2 | −23.5 | −20.7 |

192 | 334.1 | 333.5 | 331.7 | 330.7 | 324.5 | −31.6 | −28.4 | −28.3 | −25.9 | −18.7 |

224 | 333.6 | 332.1 | 331.4 | 330.9 | 329.4 | −29.8 | −24.3 | −24.1 | −24.8 | −23.8 |

231 | 328.8 | 329.3 | 326.3 | 317.1 | 308.9 | −30.3 | −30.1 | −30.1 | −19.4 | −8.9 |

_{s}_max(K) | ||||||||||
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96 | 283.2 | 283.5 | 283.9 | 304.1 | 304.6 | 316.9 | 316.9 | 314.3 | 314.3 | 314.3 |

112 | 291.6 | 290.8 | 292.5 | 306.0 | 306.1 | 321.3 | 321.3 | 319.4 | 319.1 | 315.1 |

121 | 292.4 | 291.7 | 291.9 | 297.2 | 297.9 | 318.9 | 318.9 | 318.9 | 318.7 | 312.5 |

144 | 298.3 | 300.8 | 301.6 | 302.3 | 302.3 | 329.6 | 329.6 | 326.7 | 326.1 | 323.8 |

152 | 291.9 | 293.1 | 292.7 | 295.9 | 297.2 | 328.2 | 328.2 | 327.7 | 327.0 | 322.9 |

163 | 294.2 | 294.9 | 294.9 | 300.8 | 300.6 | 330.9 | 330.9 | 329.7 | 329.7 | 324.3 |

176 | 297.7 | 300.3 | 300.6 | 306.6 | 306.7 | 334.5 | 334.5 | 331.8 | 331.8 | 331.8 |

192 | 294.6 | 296.6 | 296.8 | 303.0 | 302.6 | 333.8 | 333.8 | 332.0 | 331.8 | 326.0 |

224 | 293.1 | 295.9 | 296.4 | 305.3 | 305.4 | 336.5 | 336.5 | 331.0 | 330.8 | 328.9 |

231 | 291.4 | 291.2 | 291.3 | 297.6 | 299.4 | 329.5 | 329.5 | 323.5 | 323.5 | 312.7 |

a and b respectively represents the intercept and the slope of the dry edge

c represents the constant temperature at the wet edge and also represents the minimum surface temperature

The average of the Pearson correlation coefficient (^{−2}) and Mean of Difference (MD, W·m^{−2}) of the 10 pairs of ET estimates over the 10 days (

96 | 0.9935 | 0.9933 | 0.9940 | 1.0000 | 65.89 | 65.44 | 65.65 | 6.98 | −46.68 | −46.06 | −46.54 | −4.11 |

112 | 0.9857 | 0.9862 | 0.9878 | 0.9983 | 42.37 | 43.94 | 42,16 | 15.75 | −20.43 | −22.64 | −21.01 | 12.38 |

121 | 0.9816 | 0.9888 | 0.9888 | 0.9941 | 25.40 | 22.80 | 22.53 | 15.29 | −18.01 | −11.46 | −10.99 | 9.41 |

144 | 0.9881 | 0.9984 | 0.9989 | 0.9989 | 12.85 | 14.42 | 13.31 | 13.35 | −3.41 | 12.06 | 11.93 | 12.79 |

152 | 0.9970 | 0.9975 | 0.9975 | 0.9985 | 26.83 | 28.34 | 26.98 | 26.04 | 20.78 | 23.17 | 21.43 | 23.25 |

163 | 0.9959 | 0.9971 | 0.9967 | 0.9993 | 22.86 | 23.26 | 19.56 | 20.89 | 7.64 | 8.84 | 4.72 | 18.85 |

176 | 0.9956 | 0.9975 | 0.9973 | 0.9998 | 19.78 | 17.79 | 16.10 | 10.32 | −7.64 | −2.94 | −5.53 | 8.71 |

192 | 0.9972 | 0.9976 | 0.9983 | 0.9996 | 25.88 | 24.67 | 21.89 | 24.65 | 7.29 | 11.49 | 6.23 | 21.57 |

224 | 0.9964 | 0.9965 | 0.9969 | 0.9999 | 17.23 | 13.33 | 13.63 | 4.32 | −9.77 | −7.59 | −8.78 | 3.69 |

231 | 0.9400 | 0.9378 | 0.9489 | 0.9891 | 38.63 | 38.67 | 38.87 | 28.71 | 0.84 | 1.53 | −5.41 | 5.79 |

average | 0.9871 | 0.9891 | 0.9905 | 0.9977 | 29.77 | 29.27 | 28.07 | 16.63 | −6.94 | −3.36 | −5.40 | 11.23 |

96 | 0.9928 | 0.9926 | 0.9935 | 54.95 | 54.50 | 54.81 | −42.28 | −41.73 | −42.24 |

112 | 0.9890 | 0.9895 | 0.9909 | 32.40 | 33.96 | 32.51 | −19.24 | −21.15 | −20.14 |

121 | 0.9910 | 0.9991 | 0.9992 | 19.04 | 16.14 | 15.78 | −19.14 | −13.46 | −13.04 |

144 | 0.9927 | 0.9997 | 0.9999 | 15.84 | 4.59 | 2.36 | −13.22 | 1.38 | 0.23 |

152 | 0.9993 | 0.9996 | 0.9995 | 5.56 | 5.68 | 5.03 | 1.37 | 3.26 | 1.59 |

163 | 0.9979 | 0.9986 | 0.9984 | 13.60 | 13.16 | 13.50 | −4.25 | −3.10 | −8.63 |

176 | 0.9961 | 0.9979 | 0.9978 | 17.56 | 13.91 | 14.58 | −11.49 | −6.95 | −10.71 |

192 | 0.9980 | 0.9982 | 0.9988 | 14.67 | 10.82 | 13.89 | −7.70 | −4.91 | −10.68 |

224 | 0.9971 | 0.9973 | 0.9975 | 14.57 | 11.89 | 12.63 | −9.88 | −8.94 | −10.16 |

231 | 0.9816 | 0.9808 | 0.9861 | 21.14 | 21.58 | 18.71 | 9.00 | 9.65 | 2.65 |

average | 0.9936 | 0.9953 | 0.9962 | 20.93 | 18.62 | 18.38 | −11.68 | −8.59 | −11.11 |

d | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

96 | 1.0000 | 1.0000 | 0.68 | 0.54 | −0.37 | 0.32 | 96 | 1.0000 | 0.64 | −0.63 |

112 | 0.9999 | 1.0000 | 1.46 | 2.73 | 0.33 | −1.70 | 112 | 1.0000 | 2.04 | 1.96 |

121 | 0.9919 | 1.0000 | 1.14 | 0.44 | −1.03 | −0.43 | 121 | 0.9867 | 2.65 | −1.53 |

144 | 0.9899 | 0.9998 | 3.34 | 2.66 | −1.12 | 0.49 | 144 | 0.9930 | 2.92 | −2.11 |

152 | 1.0000 | 1.0000 | 1.86 | 1.82 | −0.89 | 1.78 | 152 | 0.9999 | 2.48 | −2.15 |

163 | 0.9999 | 0.9999 | 4.93 | 5.78 | 3.37 | 4.91 | 163 | 0.9999 | 2.01 | −1.75 |

176 | 0.9996 | 0.9999 | 4.98 | 4.14 | −1.89 | 3.16 | 176 | 0.9994 | 5.79 | −5.32 |

192 | ,0.9997 | 0.9998 | 5.53 | 5.30 | 0.80 | 4.72 | 192 | 0.9999 | 2.85 | −1.30 |

224 | 0.9996 | 0.9999 | 4.83 | 1.36 | −1.23 | 0.77 | 224 | 0.9995 | 2.94 | 0.67 |

231 | 0.9994 | 0.9991 | 6.36 | 7.14 | 5.75 | 6.27 | 231 | 1.0000 | 1.21 | −1.12 |

average | 0.9980 | 0.9998 | 3.51 | 3.19 | 0.37 | 2.03 | average | 0.9978 | 2.55 | −1.33 |