Vol.48, No. 1 2016 [601785]

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METHOD FOR THE SPATIAL INTERPOLATION OF EVAPORATION CAPACITY
FOR AGRICUL UTRAL ENVIRONMENT
/
面向农业环境的蒸发量空间插值方法

Ph.D. Yinlong JIN1), Prof. Ph.D. Eng. Jiesheng HUANG1), Ph.D. Ben LI1,2)
1)State Key Laboratory of Water Resource and Hydropower Engineering Scie nce ,Wuhan University, Wuhan /China ;
2) College of Earth, Ocean, and Atmospheric Sciences , Oregon State University , Corvallis /U.S.A.
Tel: +86-138-71136226 ; E-mail: [anonimizat]

Keywords: Agricultural environment; Waterlogging field; Evaporation cap acity; Temperature; Spatial
interpolation

ABSTRACT
Waterlogging is a common agricultural disaster with complicated causes when agricultural environment
change s, one of which is evaporation. Identifying waterlogging disasters requires evaporation data with
continuous space –time distribution. Research on the spatial interpolation of evaporation capacity facilitates
recognizing and transforming waterlogging fields and is a significant developmental direction in irrigation and
water conservancy. Traditional sp atial interpolation methods are based on the correlation between the
interpolating point and observation station. By contrast, the present study develops a new method by
conducting the following work: First, ground evaporation and air temperature are consi dered to be a field
coupled with the atmospheric flow field, which is calculated through the spectral method. A new spatial
interpolation method is proposed based on spherical harmonics and with the incorporation of temperature
parameters into the calculat ion model. Second, the internal and external errors of the interpolation results
are calculated under multiple temperature conditions, and precision evaluation and robustness analysis are
conducted on the interpolation results of the daily evaporation capa city. Lastly, a comparative analysis is
conducted on the calculation results of the monthly evaporation capacity and MOD16 data under multiple
temperature conditions. This study provides selection methods and judging conditions for temperature
parameters a nd also discusses the occurrence of the temperature accumulative effect in the interpolation of
the monthly evaporation capacity. Using the measured data in an evaporation station in Anhui Province as
an example, this study calculates the model and uses th e measured data to verify the model. Results show
that the proposed method has reasonable precision. The internal and external errors of the spatial
interpolation model of the daily evaporation capacity are about ±1mm, and those of the monthly evaporation
capacity are about ±6mm. This study also explains the contracting phenomenon of the residual distribution
and model precision, as well as the temperature accumulation phenomenon, in the interpolation of the
monthly evaporation capacity. The experimental re sults show that the method proposed in this study is a
feasible and effective spatial interpolation method to measure evaporation capacity and can provide
scientific basis for the identification and transformation of waterlogging fields and relevant farmin g and water
management practices.

REZUMAT
农田环境变化时，涝渍灾害是常见的成因复杂的农业灾害 , 蒸发是重要的致灾因素 . 渍害的识别需要时空连续
分布的蒸发量数据 , 蒸发量空间插值的研究有助于涝渍田识别及改造 , 是农田水利发展的重要方向 . 传统的空
间插值方法依据插值点与观测站之间的相关性 , 本文寻求新思路并进行了以下工作 : 首先, 从大气运动场解算
的谱方法 , 将地面蒸发和大气温度看做一个耦合场 , 提出一种基于球谐函数的空间插值新方法 , 同时将温度参
数纳入解算模型 . 再者, 计算多种温度条件下插值结果的内外符合精度 , 对日蒸发量插值结果进行精度评价和
稳健性分析 . 最后, 对多种温度条件下的月蒸发量计算结果和 MOD16 数据进行对比分析 , 给出了温度参数选
择方法判定条件 , 同时提出了月蒸发量插值计算中的温度累积效应 . 以安徽省蒸发站实测数据为例 , 进行模型
解算, 并利用实测数据进行验证 , 结果表明该方法具有合理的精度 , 日蒸发量空间插值模型的内外符合精度均
在±1mm左右, 月蒸发量内外符合精度均在± 6mm左右. 同时解释了残差分布与模型精度的相悖现象和月蒸
发量插值中的温度累积现象 . 实验结果表明本文研究方法是一种可行且有效蒸发量空间插值算法 , 可为渍害田
识别改造及相关农业水管理实践提供科学依据 。

INTRODUCTION
Many studies focus on agriculture environment , where the long -term saturation state of soil moisture in

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the crop root system restricts crop growth and reduces crop productivity (Qian and Wang , 2015). Field
evaporation is a key link in the water circulation process and a significant component of water circulation.
Along with rainfall and runoff, it determines the hydrologic balance in a region and directly influences
farmland environment. Under certain topographic and rainfa ll conditions, a continuously low evaporation
capacity results in long -term soil water saturation. This then leads to waterlogging disasters and causes crop
failure, while a continuously high evaporation would result in droughts as well as crop failure. He nce,
changing the process and features of evaporation capacity is the main basis for field water applications and
management, and research on evaporation capacity is of great importance to agricultural production (Su and
Feng , 2015) .
At present, many metho ds to calculate evaporation capacity are available. The most direct method is
the instrument measurement method, which involves the use of an evaporation pan and land evaporator to
directly measure the evaporation capacity. In the case of insufficient or l ack of measured data, the indirect
method can also be used to estimate the evaporation capacity. The methods with the broadest application
are the Penman –Monteith (P-M) formula, which is the only standard for calculating ET0 suggested by Food
and Agricultu re Organization of the United Nations (FAO), and the Hargreaves (H-S) formula, which can
calculate the daily ET0; the former requires seven meteorological factors, and the latter needs four
meteorological factors. Moreover, remote sensing technology, toge ther with meteorological data, under a
certain assumption, may employ the water -vapour balance equation, geostatistics theory, or all kinds of
regression methods to conduct spatial interpolation and thereby estimate the evaporation capacity within a
large scale (Hassan , 2012) . The aforementioned methods have their own advantages and limitations. When
empirical methods, such as the P -M formula, are used, the physical conditions of various regions must
necessarily be considered. Hence, such methods are quite difficult to apply when the evaporation capacity
has a large variation. When remote sensing inversion or the water -vapour balance equation is used to
estimate the evaporation capacity, the model needs multiple parameters with a complicated model structure.
The development of remote sensing and GIS technology can realize the acquisition of large -scale
evaporation capacity data; however, such acquisition remains very difficult to realize given continuously
changing large -scale evaporation capacity data and th e restrictions imposed by ground data and
meteorological conditions (Raghuveer et al. , 2011 ; Paul et al. , 2012 ).

Fig.1 – Distribution diagram of the inversion results for the waterlogging field

Waterlogging control, drought resistance, and disaster r eduction have always been important in the
field of agricultural production research. Fig. 1 shows the inversion results of using evaporation data with
continuous space –time distribution and other multi -source data on waterlogging fields in Anhui Province (Jin
et al, 2014) . Many spatial interpolation methods exist, such as the Thiessen polygon, spline function method,
inverse distance weighted (IWD), Kriging, spatial interpolation model of artificial neural network (BPNNSI),
and so on. The relevant assumpti ons of the aforementioned methods are based on the spatial distribution
and location of evaporation capacity, which is then solved by the methods by considering the other factors
that influence it (Cha , 2011). The results obtained are limited to some data of observation stations near the
interpolation point with obvious uncertainty. The present study proposes a spatial interpolation method
based on the spherical function, which considers evaporation capacity as a field covering the whole
interpolation area, and the using spectral method to solve the overall parameters. It also integrates

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temperature data to further reduce the uncertainty of the calculation results (Tian , 2012). Anhui is located in
a transitional area of warm temperature zone with an average annual temperature of 14 –16 °C and a
temperature difference of 2 °C between the south and north.

MATERIAL AND METHOD
Data source
The temperature dataset “China daily surface air temperature value 0.5°×0.5°grid point dataset (V2.0)”
was downloaded from th e Chinese meteorological data shared service network, and the basic
meteorological element data from 2,472 open sea stations (i.e., excluding Xisha and Coral Island) and from
the latest national -level surface meteorological stations reorganized on the basi s of special database.
The evaporation capacity data were derived from two sources. The first source was the daily
evaporation capacity data from 26 meteorological stations in Anhui Province downloaded from the Anhui
drought severity information network. T he second dataset, the MOD16 data (transpiration product) provided
by MODIS with a spatial resolution of 1 km for a period of months , could be directly downloaded from the
website provided by MODIS. The MOD16 data from May to August of 2013 were selected f or the experiment
in this study.
Data preprocessing
The downloaded temperature data consisted of ASCII coded documents, which could directly be read.
The transformation of the format and spatial data had to be conducted, and the internal grid data files (* .img)
supported by the ARCGIS platform were generated. The MOD16 data were also subjected to file format
transformation, reprojection, and splicing, and clipping work, depending on the ARC GIS platform. The spatial
datum was introduced for the convenience of analysis in this study. The spatial datum involved in this paper
consisted of GCS_WGS_1984.
Spatial interpolation method based on the spherical function
The research on evaporation began with bare land evaporation, using the empirical and mechanism
method . The development of this line of research showed,that the evapotranspiration problem of crops was
closely related to bare land evaporation. Researchers introduced the energy balance method and water
vapor diffusion theory to the research on evapotranspira tion. The evapotranspiration quantity of crops is
considered to indicate the process of energy consumption; the water yield consumed by crop
evapotranspiration is calculated through energy balance (Li et al. 2013 ; Yang , 2011).
Based on the aforementioned a nalysis, various corresponding transpiration formulas are available for
different phases of crop evapotranspiration. Under normal conditions, the calculation of evaporation on bare
soil uses the formula similar to that of crops:

12() E k e e (1)
where
E is the crop evapotranspiration quantity in mm;
k is a constant;
1e is the saturation vapo r
pressure; and
2e is the actual vapor pressure in hPa.
Based on the Magnus formula (2),
1e is a function of temperature:

7.45
273.16
16.1 10t
te (2)
where t is the daily average temperature in °C. Within the variation range of the meteorological
temperature, the Magnus formula can be replaced by a straignt line, and Equation (2) is transformed into

1e Ct D (3)
In Equation (1), the variation of the absolute value of
2e is smaller than that of
1e , and its absolute
value can be expressed with a constant. The above eq uation is substituted into (1), and the following can be
obtained:

E mt n (4)
As shown above, the direct factors that influence the calculation of transpiration involve air pressure and
temperature, so that atmospheric factors, such as temperature, should be considered in the spatial
expansion of the transpiration data. The models used to predict evapotranspiration are divided into two
types: The first involves direct cal culation, such as the air humidity method, temperature wind speed method,
and others; the second involves the determination of the total evapotranspiration quantity and crop factors of

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the reference crop, such as the P-M formula, complementary correlation theory, SPAC theory,
evapotranspiration method for the reference crop, remote sensing method, and so on (Lagos et al. , 2013 ;
Seitz , 2008) . This study considers evaporation to consist of a field covering the surface of the earth and uses
the spherical funct ion model to solve the parameters of this field to realize the expansion of the evaporation
data from a single observation station to continuous coverage.
The spherical function has been widely applied to the resolution of field equations, such as earth
physics and atmospheric motion, among others. Compared with the classical grid method, the spectral
method of the spherical function features high precision, good stability, and simple resolution (Tolk , 2015 ;
Seitz , 2008) . The spherical function is adopted i n this study to establish the basic model. By considering the
relationship between evaporation and temperature, spatial distribution models (with or without consideration
of temperature) are established, and the resolution results are then analyzed.
When t he influence of temperature is not considered, the evaporation calculation model can be called a
purely spherical function model and is expanded into the following form:

max
( , )
00(sin )( cos( ) sin( ))n n
s nm nm nm
nmET P a ms b ms 

(5)
where
( , )s ET is the evapotranspiration in the observation station;
maxn is the spherical function
phase;
( , )nm nmP n m P
is the normalized Legendre polynomial;
 is the normalized function;
nmP is
the normalized Legendre function;
( , )s is the geographic latitude and longitude of the observation
station; and
nma and
nmb are the coefficients to be resolved.

2 1 ( )!21 ( )!nm
nmn n m
nm   (6)
In the equation,
nm is the Kronecker function.
Considering the influence of temperature factors on evapotranspiration and the relationship expressed
in Equation (4), the influence of temperature is integrated into Equation (5), and it can be called the
expandable spherical function model, as shown in the following equation:

max
( , )
00(sin )( cos( ) sin( ))n n
s nm nm nm
nmET P a ms b ms kT 
  
(7)
where
T is the temperature of the observation station, and
k is the coefficient to be resolved. The
other symbols are also found in Equation (5).
Model resolution
The specifc flow of the model resolution flow is shown in Fig. 2.
Longitude and Latitude of
the Observation Station
Temperature of the
Observation Station
Evaporation Capacity of
the Observation Station
Model Parameters
Dispersive Interpolation
Region
Evaporation Capacities of the
Dispersion Points
Information of the
Dispersive Points

Fig.2 – Flow chart of the model resolution

The specific steps of the model resolution are as follows: First, the spatial analysis function of ARCGIS
software is used to extract the temperature data. Second, the parameters in Equati on (5) and (7) are
re-resolved with the combination of the longitude and latitude and the measured value of evaporation. One
group of parameters corresponds to one day. A total of nine coefficients are used when the temperature is
not considered, and ten w hen the temperature is considered. The administrative region in An’hui Province is
then dispersed, and the longitudinal and latitudinal coordinates and temperature values at the dispersed

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point are obtained. The evaporation capacity at this point is determ ined according to the parameters.

RESULTS
Model precision analysis
To evaluate the effectiveness of this model, the data from 23 observation stations, which are evenly
distributed among the 26 observation stations in Anhui Province, are adopted to conduc t mathematical
modelling and calculation. The other three are used to conduct externally coincident inspections and to
measure the precision of the model. Considering five day’s worth of data from August 25 to 29, 2013, the
compensating computation of the two models is established. The statistical information of the residual
absolute error value is shown in Table 1, which compares the externally coincident precision of the IDW and
KRIGING methods under the same resolution conditions.
The internal error is t he precision obtained through the compensating computation under optimal
estimation is also called the mean square error
ˆ of the unit weight:

ˆ()TV PVnt (8)
where
V is the residual error of the evaporation capacity in the observation station involved in the
adjustment calculation , n is the number of observed values and is set as 23, and t is the observed quantity.
The extern ally coincident precision is obtained by calculating the data in the observation station of the
externally coincident inspection. The calculation formula is as follows:
3
1()
ˆ
3ass real
k
EAAET ET


(9)
Where
ˆEAA is the externally coincident precision;
assET is the estimated model value of the
evaporation capacity in the observation station; and
realET is the known observed value in the observation
station.
Table 1
Statistical table of the absolute values of the residual error and precision indexes (unit: mm)
Spherical
Function Time
1v
1 1.5v
1.5 2 v
2v IE EE OM EE
Temperature
Not
Considered
(SHTNC) 1st day 82.6% 13.0% 4.4% 100% 0.92 1.45
IDW 1.82
2nd day 78.3% 21.7% 0% 100% 0.99 0.90 1.79
3rd day 87.0% 4.4% 4.4% 95.8% 1.01 0.48 1.81
4th day 87.0% 13.0% 0% 100% 0.83 0.53 1.73
5th day 82.6% 8.7% 8.7% 100% 0.97 0.94 1.77
Temperatrue
Considered
(SHTC) 1st day 95.6% 0% 4.4% 100% 0.94 1.43
KRIG
ING 1.85
2nd day 73.9% 26.1% 0% 100% 1.03 1.07 1.72
3rd day 91.3% 0% 4.4% 95.7% 1.04 0.77 1.79
4th day 91.3% 8.7% 0% 100% 0.88 0.49 1.63
5th day 82.6% 8.7% 8.7% 100% 1.04 0.96 1.75

The
v represents the absolute value of the residual error after the compensating computation of the
model. Table 1 shows the statistics of the percentage of the absolute values of the residual error and the
number of thos e involved in the calculation of the model. Based on Table 1, most of the absolute values of
the residual error are superior to 1 mm; those over 90% are less than 1.5 mm; and those consisting of only
several data points are greater than 1.5mm. Generally sp eaking, both the two models can satisfy the
requirements of the spatial interpolation of the evaporation capacity. Regardless of the adjustment and
residual error of the model, or the internal and external errors, the numerical values are quite close to on e
another. The data from columns 8 and 10 in Table 1 are also compared. The external coincident precisions
of the two models adopted in this paper are superior to the corresponding values of the IDW and KRING
methods.
Careful analysis shows that an inconsi stency exists between the distribution laws of the residual error
and the precision of the two models. As shown in Table 1, among the continuous five -day interpolation

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results, with the exclusion of the two -day results, the results from the other four days do not conform with the
law that a good residual error distribution corresponds to good model precision. The residual errors with
absolute values of less than 1 mm correspond to the spatial interpolation model that considers the
temperature and appear mor e frequently. The model precision indexes are low, and the highest proportion of
the residual errors with absolute values of less than 1 mm of the model that considers the temperature is
95.6%. By contrast, the corresponding value of the model that does no t consider temperature is 82.6%.
Thus, the difference between the values of the two is 13.0%. For the internal error, the former is 0.94, and
the latter is 0.92. For the external error, the former is 1.43, and the latter is 1.45. What is worth mentioning is
that the residual error distribution corresponds to two interpolation models that are consistent, while the
precision index of the model that considers temperature is slightly lower.
Model precision and reliability are two significant indexes for evaluat ing the interpolation model. Aside
from being influenced by their own functional precision, the resulting interpolation precision is also
influenced by the precision of the adopted parameters. Generally speaking, the more parameters the model
involves, the lower the interpolation results precision are. However, adopting reasonable parameters can
enhance model reliability. Temperature parameters are introduced to the spatial interpolation model that
considers temperature. Although this slightly lowers the mo del precision, it optimizes the distribution laws of
the residual error, thereby improving model reliability. In terms of the interpolation results of the daily
evaporation capacity, the influence of temperature cannot be highlighted because of the small d aily
evaporation capacity.
Analysis of the precision of the monthly evaporation data and selection of temperature data
The spherical model is used to conduct the spatial interpolation of the daily evaporation capacity from
May to August, 2013. The monthly evaporation capacity is then calculated. When the expanded model is
used to conduct spatial interpolation, three kinds of temperature data are selected: the daily average
temperature, daily maximum temperature, and mininum temperature. By contrast, when t he temperature is
not considered in the calculation, four kinds of interpolation results can be obtained.

Fig.3 – Comparative diagram of the average temperature interpolation results and MOD16

For 50 randomly generated inspection points, four kinds of i nterpolation data corresponding to the
inspection points are extracted. With the MOD16 data corresponding to the inspection points as the truth
value of the evaporation capacity, 37 inspection points data are reserved after the abnormal points on the
water surface and urban and town areas are excluded; the variances are calculated and listed in Table 2. A
correspondence diagram between the monthly evaporation capacity and MOD16 data, which are obtained
by adopting the daily average temperature interpolation , is shown in Fig. 3. A comparative diagram between

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the expanded model and purely spherical function model under the four situations is shown in Fig. 4.
As shown in Fig. 3, the comparison of the monthly evaporation capacities is resolved by expanding the
model, which adopts the daily average temperature and MOD16 data. The red line represents the
interpolation results, and the blue line represents the MOD16 data. The variation tendencies of the two are
consistent, and the interpolation results only jitter u p and down the MOD16 data. The maximum error is less
than twice the variance. Fig. 4 compares the monthly evaporation capacities of the spherical function models
under the four situations. The graph entities for May and July are consistent, but some inspec tion points
exhibit large deviation in June. A large fluctuation with opposite chang e tendencies occurs in August
(Bezborodov et al. 2010, M.P. Gonzalez et al. 2009) . Combining the variance data of the evaporation
capacities at the inspection points in Tab le 2, the interpolation data variance in the expanded model, which
uses the daily average temperature, remains stable and small. By contrast, the variances in the interpolation
data in other forms are not stable enough. Thus, adopting the daily average tem perature as the parameter of
the interpolation model can result in relatively ideal interpolation results.
Table 2
Statistical table of the variance in the monthly evaporation data (unit: mm)
Month Daily Max
Temperature Daily
Average
Temperature Daily Min
Temperature Temperature
Not
Considered Evaporation
Max Error MOD1
6
5 6.10 5.98 6.37 6.91 -12.30 93.8
6 4.94 5.05 5.25 7.72 12.25 72.5
7 5.01 5.18 5.47 5.98 -11.72 127.3
8 6.64 5.74 7.51 9.16 14.44 115.0

Given the major hopping position in Fig. 4, it is necessary to analyze the characteristics of the
temperature data at the test point to study whether the model is practicable for the temperature data.. The
variance of the model, which takes the average temperature in Table 2 as parameter, is considered to be the
threshold value. The inspection point with an error smaller than the threshold value follows a consistent
trend, and the inspection point with an error larger than the threshold value is deviation positions. And then
the calculation of the stati stics of the consistent and deviant positions of the trend corresponding to each
month is needed.

Fig.4 – Comparative diagram of the interpolation results under the four situations

The average maximum temperature, average temperature, average minimum te mperature, difference
between the average maximum and average minimum temperatures, difference between the average

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maximum and average temperatures, maximum temperature difference at consistency, and minimum
temperature difference at deviation are listed i n Table 3.
Table 3
Statistical table of the temperature data characteristics at the inspection points (unit: °C)
M MAMaxT AMT MAMinT MaxTD MaxATD MaxTD C MinTDD
5 26.71 21.59 17.21 9.50 5.12 4.98 6.47
6 28.45 24.27 20.98 7.47 4.18 3.12 8.58
7 33.99 32.73 30.12 3.87 1.26 4.10 6.23
8 34.29 31.65 25.41 8.88 2.64 3.69 8.98
Note: M: month; A: average ; T: temperature ; D: difference; DC: difference at consistency; DD: difference at deviation

The data volume matrix in Table 3 is established, and its correlati on coefficient matrix is solved. The
correlation between columns 7 and 8 in Table 3 with the proceeding columns is observed, and the maximum
correlation coefficient is 0.42. Hence, the model interpolation effect does not have any significant linear
correla tion with the overall variation range of the temperature data or with the temperature. The correlation
coefficient between columns 7 and 8 is -0.76, which is a significantly negative correlation. Hence, the data in
columns 7 and 8 in Table 3 are combined a nd taken as the indexes of the model's resistance capability to
temperature variations; that is, the interpolation effect is good when the temperature variation is within
3.12 °C, but is poor when the temperature variation is above 6.23 °C.
The monthly eva poration interpolation is calculated by transforming the multiple temperature
parameters. Through the comparative analysis of the interpolation results and the continuous space –time
distribution features of the MOD16 data, the adoption of the daily average temperature can obtain the
optimal solution of the model. The variance in the optimal value is taken as the threshold value to classify the
interpolation results. The maximum temperature difference at consistency (TDC) and minimum temperature
difference a t deviation (TDD) can also be obtained. These two are correlated with the interpolation results
and can serve as the indexes to evaluate the temperature difference resistance capacity and the applicability
of the model.
Accumulation effect of the daily eva poration capacity with consideration of the temperature
The expanded spherical function model, which considers the temperature, produces the accumulation
effect of the daily evaporation capacity (Miguel et al. 2011). The comparation and analysis of the MOD 16
data in August with the accumulation effect had been made. As shown in Fig.5, A represents the
accumulated monthly value of the spatial interpolation of the daily evaporation with out consideration of the
temperature, B represents the value with consider ation of the temperature, and C represents the MOD16
data.

Fig.5 – Monthly cumulative comparison of the spatial interpolation of the evaporation capacity

The overall evaporation data in Fig. 5A are low. Meanwhile, the evaporation distribution in Fig. 5 B more
closely approaches the data in Fig. 5C than those in Fig. 5A, the evaporation data to the east and west of
Anhui Province are higher than those in the corresponding areas in Fig. 5A, which embody the accumulation
effect of the spherical function mod el that considers the temperature. Based on the statistical data of the
monthly evaporation capacity during the 4 -month spatial expansion in 37 inspection points examined in this
study, the temperature accumulation effect may indicate that the sum of the m onthly evaporation capacities
in the inspection points obtained by the model resolution corresponds to each temperature parameter minus

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those obtained by the model resolution that does not consider temperature. The difference values are listed
in Table 4; column 1 represents the month, columns 2 to 4 represent the difference values of the evaporation
capacity, column 5 represents the sum of the evaporation capacities of the inspection points of the model
that does not consider temperature, and column 6 repr esents the MOD16 data.
Table 4
Statistical table of the difference values of the monthly evaporation capacity and relevant data (unit: mm)
Month Max
Temperatu
re Average
Temperatu
re Min
Temperatu
re Temperature Excluded MOD16
5 5.48 4.32 0.09 2338.568 2346. 4
6 22.60 19.48 19.30 2550.447 2591.9
7 35.25 18.49 16.27 4292.903 4263.4
8 9.23 49.67 77.67 3976.740 3998.2

Based on Table 4, the sum of the monthly evaporation capacities in all the months under all the
temperature parameters are greater than the su m of the monthly evaporation capacities resolved by the
model that does not consider temperature. This indicates that the model that considers temperature has a
temperature accumulation effect. The difference value matrix of the evaporation capacities from columns 2
to 4 in Table 4 and the temperature data matrix from columns 2 to 4 in Table 3 are established. The
correlation coefficient between the two matrices is 0.251, which indicates that the linear correlation between
the temperature accumulation effec t and temperature is not obvious. The correlation coefficient between
columns 5 and 6 in Table 4 is 0.997, which indicates that the resolution of the function model has a
significant correlation with the MOD16 data.
The temperature accumulation effect exis ts in the interpolation of monthly evaporation data. However, it
is restricted by the spatial density of temperature, observed evaporation value, and data precision.
Moreover, given the complicated relationship between temperature and evaporation capacity, this study
does only little to reveal the temperature accumulation phenomenon, which should be the focus in future
studies.

CONCLUSIONS
To satisfy the requirements of the agricultural environment study for continuous space –time distribution,
the cal culation of the evaporation spatial interpolation should not be limited to traditional methods, and
relevant multi -source information must necessarily be integrated.
This study proposes a new method for the spatial interpolation of the evaporation capacit y. It then uses
actual measured data in Anhui Province and national temperature field distribution to verify the proposed
method and at the same time analyses the influence of the temperature field on the interpolation results.
The following conclusions c an be drawn from the study:
– Error analysis indicates that this method has high precision and is superior to the pure IDW and KRIGING
methods. The introduction of temperature parameters results in inconsistencies between the distribution
law of the residual error of the interpolation results and the internal and external errors. This occurs
because, after the temperature parameters are introduced to the spatial interpolation model, the errors of
the temperature parameters are propagated and affect the model precision. However, the interpolation
results lead to a more optimal distribution, thereby enhancing the reliability of the model ;
– Based on the analysis, the TDC and TDD are correlated with the interpolation results. They can serve as
indexes for the model temperature difference resistance ability and evaluation of the model applicability.
Taking the MOD16 monthly evaporation capacity with continuous space –time distribution features as the
control, this paper analyses the monthly evaporation interpolation r esults under multiple temperature
values and adopts the daily average temperature to conduct model resolution and obtain the optimal
solution ;
– In the calculation of the spatial expansion of the monthly evaporation capacity, the model that considers
tempera ture exhibits the temperature accumulation effect phenomenon , and it has a more complicated
relationship with the daily evaporation data.
This study satisfies the required evaporation data for agricultural environment and provides a reference
and basis for the calculation of field evaporation data and analysis of the relationship between tem perature
and field evaporation. This promotes farmland water management and utilization, as well as relevant
progress in agricultural production. However, evaporation, w hich is a complicated natural phenomenon, has

Vol.48, No. 1 / 2016

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a complex relationship with factors, such as altitude, wind speed, and temperature. Further analysis must be
conducted on the influence of all these factors on the method proposed in this study.

ACKNOWLEDGEME NT
The work was supported by the National Science and Technology Pillar Program during the 12th
“Five -Year Plan” Period ( Project No.: 2012BAD08B03 -4)

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