Using the Fuzzy Clustering and Principle Component Analysis for Assessing the Impact of Potential Evapotranspiration Calculation Method On the Modified RDI Index

The modified reconnaissance drought index (RDIe) which is a modified version of RDI is presented for assessing drought conditions with an emphasis on agricultural drought. The potential evapotranspiration (PET) and effective rainfall are required climatic variables to calculate RDIe. Although the FAO Penman–Monteith (FPM) equation is the reference method for determining the PET, due to the need for data of a large number of climatic variables it is difficult to use in areas with shortage climatic data. Therefore, in this research, using the fuzzy clustering (FC) and principle component analysis (PCA) methods, the influence of PET calculation methods including FPM (used as reference method), FAO Penman (FP), Hargreaves-Samani (HS), Blaney-Criddle (BC), Turc (Tu), Jensen-Haise (JH), Priestley–Taylor (PT) and FAO24 Radiation (Ra) methods on the RDIe (in 1, 3 and 12-month time scales) was assessed. In this study the climatic data series of 5 stations in Fars province, Iran from 1989 to 2018 was used. Based on the results of PCA model, in short-term time scales (1 and 3-month), the calculated RDIe values based on the HS method (at 100% of stations) and in long-term time scale (annual) based on the FP method (at 60% of stations) had the highest correlation with RDIe based on the FPM method. According to the results of FC method, in 1-month time scale, the values of RDIe using PT and HS methods (at 100% and 80% of selected stations, respectively), in 3-month time scale, the values of RDIe using PT, HS and Ra methods (at 100% of stations) and in annual time scale, the values of RDIe using FP method (at 60% of stations) had the highest similarities with the values of RDIe using FPM. Therefore, it is recommended to replace the FPM method with HS (in 1 and 3-month time scales) and FP (in 12-month time scales) methods in areas with minimum available meteorological data.

     

基于信息熵原理的东北地区参考作物蒸散量时空特征分析

根据1951—2013年东北地区116个气象站点的常规气象资料,基于信息熵理论构建了东北地区日参考作物蒸散量站点间的信息传输模型并分析了信息场的分布情况,利用聚类分析法解析了东北地区日参考作物蒸散量的区域相似性结构特征;并在此基础上选取6个代表性站点,运用重标极差法分析了参考作物蒸散量(ET_0)的时间分形特征。结果表明:空间上,东北地区日参考作物蒸散量的信息熵随纬度增加而减小,各站点信息传输指数随基站与辅站距离的增大而减小,且具有明显的各向异性;东北地区在站点群层面上的信息传输总体呈由南到北、由东到西的分布规律。时间上,东北地区多年平均ET_0总体呈下降趋势,哈尔滨、沈阳、赤峰、加格达奇、佳木斯、海拉尔6个代表性站点的ET_0在未来一定时段内的变化趋势趋于稳定且具有较强的持续性。     

Assessment of Blaney-Criddle Equation for Calculating Reference Evapotranspiration with NOAA/AVHRR Data

Reference evapotranspiration (ET₀) data are desirable for assessing crop water requirements and irrigation needs. A large number of methods have been developed for assessing ET₀ from meteorological data. In several places of the world, the existing network of weather stations is insufficient to capture the spatial heterogeneity of this variable The purpose of this work is to investigate whether it is possible to attain reliable estimation of ET₀ only on the basis of the remote sensing-based surface temperature (T_s) data by Blaney-Criddle (B-C) model under a semi arid environment of Iran. This study has assumed that the daytime surface temperature at the cold pixel obtained from the AVHRR/NOAA sensor can be used instead of air temperature in the Blaney-Criddle (BC) equation for ET₀ estimation in irrigated area. For this purpose, 61 NOAA- AVHRR satellite images acquired between June and September in 2004 and 2005 and weather data measured at two weather located in two irrigation regions with sugar cane located in Khuzestan plain in the southwest of Iran were used to calibrate and test the B-C model. The FAO-56 Penman–Monteith model was used as a reference model for assessing the performance of the calibrated BC model. The results show that calibrated B-C model provided close agreement with the reference values, with an average RMSE of 1.0 mm day^?1and a R² of 0.91.     

Developing Equations for Estimating Reference Evapotranspiration in Australia

Quantifying reference evapotranspiration (ET₀) is essential in water resources management. Although, many methods have been developed with different level of accuracy, in this study, two new equations were developed and optimized for estimating ET₀ using Honey-Bee Mating Optimization (HBMO) algorithm. The first eq. estimates ET₀ from extraterrestrial radiation (R_a), relative humidity (RH) and mean daily temperature (T_mean), while the second uses the same parameters except that mean daily temperatures is replaced with maximum daily air temperature (T_max). Both equations were developed using climatic data from eight weather stations in Western Australia and subsequently verified using data from ten sites across Australia. The estimated ET₀ values from both equations versus the FAO56-Penman-Monteith have a coefficient of determination, R², of larger than 0.96. Moreover, the performance of six commonly used methods of estimating ET₀ including Hargreaves-Samani, Thornthwaith, Hamon, Mc Guinness-Bordne, Irmak and Jensen-Haise were assessed and the Hargreaves-Samani method performed better than others. An attempt was made to calibrate the Hargreaves-Samani equation; however, its overall performance did not improved and the two newly proposed equations are suggested to be used in Australia.     

内蒙古东部牧区缺测数据条件下适宜ET_0计算方法优选

内蒙古东部牧区多地处偏远边疆,气象站点有限,应用FA056 Penman-Monteith计算ET0相对困难。为了在缺测气象数据条件下准确计算ET0,本文依据该区内典型气象站点资料,以FAO56 Penman-Monteith为标准方法,以FAO17 Penman、Priestley-Taylor、Irmark-Allen拟合法、Hargreaves-Samani法为对照方法分别对ET0进行计算,并对4种方法适用性进行评价。结果表明:Priestley-Taylor与Hargreaves-Samani法计算值较FAO56 PM法计算结果偏大,不适于该地区ET0计算。FAO17 Penman法和Irmark-Allen拟合法与FAO56 PM法计算结果平均相对误差小于15%,计算精度较高,但Irmark-Allen拟合法仅需气温和日照时间气象资料,因此,Irmark-Allen拟合法适宜缺测气象条件下内蒙古东部牧区ET0计算。     

西藏高海拔地区气象数据缺失条件下的ET0计算研究

西藏高海拔地区低氧低压(平均不足海平面的2/3)、太阳辐射强(年太阳辐射6 000~8 000 MJ/m2)、近地层空气湿度变化大,加之西藏地区气象资料系列短、站点少,该地区ET_0计算具有特殊性及不便性。本研究基于西藏地区9个典型站点20年逐日气象资料,通过引入海拔因子与修正温度常数对Hargreaves(HS)模型进行改进,旨在得到一种少参、准确的高海拔地区ET_0简易计算方法。结果表明,海拔2 000 m以上地区Hargreaves-Elevation(HS-E)改进模型在不同时间尺度条件下的修正结果均明显优于HS模型且避免了原HS模型在高海拔地区ET_0计算出现负值的情况,提升了ET_0计算值的实用性与精度。以PM模型ET_0计算值为标准进行误差分析,HS-E模型逐日ET_0计算的纳什效率系数(NSE)、均方根误差(RMSE)和平均相对误差(MRE)分别为0.8、0.53mm/d和13.80%,逐月ET_0计算的NSE、RMSE和MRE分别为0.84、11.90 mm/month和12.50%;对比不同时间尺度条件下(日、月)误差分析结果可知,计算时间尺度越大HS-E模型结果越优。HS-E改进模型在高海拔地区适应性较强,具有较高的计算精度,可作为西藏海拔2000 m以上地区气象数据缺失条件下ET_0计算的推荐模型。     

Fuzzy Genetic Approach for Estimating Reference Evapotranspiration of Turkey: Mediterranean Region

The applicability of fuzzy genetic (FG) approach in modeling reference evapotranspiration (ET₀) is investigated in this study. Daily solar radiation, air temperature, relative humidity and wind speed data of two stations, Isparta and Antalya, in Mediterranean region of Turkey, are used as inputs to the FG models to estimate ET₀ obtained using the FAO-56 Penman–Monteith equation. The FG estimates are compared with those of the artificial neural networks (ANN). Root mean-squared error, mean absolute error and determination coefficient statistics were used as comparison criteria for the evaluation of the models’ accuracies. It was found that the FG models generally performed better than the ANN models in modeling ET₀ of Mediterranean region of Turkey.     

汉江上游流域潜在蒸散量敏感性分析

为研究全球变暖背景下汉江上游流域潜在蒸散量的变化特征,根据汉江上游流域1960—2015年汉中、石泉和安康3个气象站的逐日实测气象数据,采用彭曼-蒙蒂斯方程计算逐日潜在蒸散量ET_0。应用敏感性公式计算ET_0对5个主要气象因子的敏感系数,并结合气象因子的多年相对变化分析ET_0变化成因。结果表明:受太阳周年运动及地形等地理要素的共同影响,汉江上游不同气象因子及ET_0的年内分布不一;汉江上游ET_0对相对湿度最为敏感,各气象因子年敏感系数多呈显著下降趋势,敏感程度均达到"中"以上等级;ET_0同气象因子表现出复杂非线性关系,日照是汉中站ET_0变化的主导气象因子,石泉和安康站ET_0变化的主导气象因子是相对湿度。     

Spatio-temporal Calibration of Blaney–Criddle Equation in Arid and Semiarid Environment

Estimates of reference evapotranspiration (ET_o) are widely used in irrigation engineering to define crop water requirements. A major drawback to application of the FAO Penman-Monteith is the relatively high data demand which unfortunately, for many locations; such meteorological variables are often incomplete and/or not available. Alternatively, the Blaney–Criddle (BC) equation is a simpler method for ET_o estimation. In this study, the BC equation was calibrated using three methods: spatially calibration at each station for the whole period (ET_o-BC_S); two periods calibration (ET_o-BC_S2); and spatial and temporal calibration at each station for each month (ET_o-BC_S,T) using twelve stations a cross Jordan. The calibration coefficient of BC equation (a, b) were determined at all stations. The results of the calibration methods showed that: (1) the spatial calibration of BC had the highest RMSE, and ME and Lower R² comparing to spatial and temporal calibration and two periods calibration. (2) Improvement was achieved for the BC equation when considering the spatial and temporal calibration for all months at each station. The values of a were negative for all months of any station. The higher values of a are coincided with cold or low temperature months while the high values coincided with high month temperature. The b values were positive for the whole stations and months. As the a values, it seems that b values had higher values in warm months than the cold one. A relatively good improvement could be obtained using two periods calibration instead of one period. The maps of a and b clearly show that a and b varied considerably in the study area and being aware of the spatial temporal variations of climatologically parameters is important in managing the limited water resources. Knowing the spatial temporal changes of such parameters, accurate calculations of ET_o can be achieved which will lead to precise and elevate water resources management in the arid region such as Jordan.     

Estimation of Monthly Mean Reference Evapotranspiration in Turkey

Monthly mean reference evapotranspiration (ET ₀ ) is estimated using adaptive network based fuzzy inference system (ANFIS) and artificial neural network (ANN) models. Various combinations of long-term average monthly climatic data of wind speed, air temperature, relative humidity, and solar radiation, recorded at stations in Turkey, are used as inputs to the ANFIS and ANN models so as to calculate ET ₀ given by the FAO-56 PM (Penman-Monteith) equation. First, a comparison is made among the estimates provided by the ANFIS and ANN models and those by the empirical methods of Hargreaves and Ritchie. Next, the empirical models are calibrated using the ET ₀ values given by FAO-56 PM, and the estimates by the ANFIS and ANN techniques are compared with those of the calibrated models. Mean square error, mean absolute error, and determination coefficient statistics are used as comparison criteria for evaluation of performances of all the models considered. Based on these evaluations, it is found that the ANFIS and ANN schemes can be employed successfully in modeling the monthly mean ET ₀ , because both approaches yield better estimates than the classical methods, and yet ANFIS being slightly more successful than ANN.     

节水灌溉稻田蒸散时空尺度特征及影响因素

为研究节水灌溉稻田蒸散规律和尺度特征及其影响因素的尺度依赖性,用小型蒸渗仪和涡度相关仪分别测量了节水灌溉稻田冠层蒸散量(ETCML)和田间尺度蒸散量(ETEC),分析了ETCML和ETEC的典型日和逐日变化规律,以及在小时和日时间尺度上的影响因素。结果表明:节水灌溉稻田ETCML和ETEC变化规律基本一致,但白天ETCML均大于ETEC,且上午两尺度蒸散量大小和相位差均明显大于下午,夜晚ETCML和ETEC接近0,但ETCML呈正负交替波动。两尺度蒸散量的逐日变化总体上呈先增加后减小,高峰期出现在分蘖后期,抽穗开花期较小。ETCML日均值大于ETEC,比值平均为1.50。净辐射和饱和水汽压差是不同时空尺度蒸散量的显著影响因素,但叶面积指数、空气温度、风速和土壤含水率对不同时空尺度蒸散量的影响不同,具有明显的时空尺度效应。     

Comparison between M5 Model Tree and Neural Networks for Estimating Reference Evapotranspiration in an Arid Environment

This paper describes a detailed evaluation of the performance and characteristic behaviour of feed-forward artificial neural network (ANN) and M5 model tree for estimating reference evapotranspiration (ET₀) at four meteorological sites in an arid climate. The input variables for these models were the maximum and minimum air temperature, air humidity and extraterrestrial radiation. The FAO-56 Penman–Monteith model was used as a reference model for assessing the performance of the two approaches. The results of this study showed that the ANN estimated ET₀ better than the M5 model tree but both models performed well for the study area and yielded results close to the FAO56-PM method. Root mean square error and R² for the comparison between reference and estimated ET₀ for the tested data using the proposed ANN model are 5.6 % and 0.98, respectively. For the M5 model tree method these values are 8.9 % and 0.98, respectively. The overall results are of significant practical use because the temperature and Humidity-based model can be used when radiation and wind speed data are not available.     

Subset Modeling Basis ANFIS for Prediction of the Reference Evapotranspiration

The study investigates accuracy of a new modeling scheme, subset adaptive neuro fuzzy inference system (subset ANFIS), in estimating the daily reference evapotranspiration (ET₀). Daily weather data of relative humidity, solar radiation, air temperature, and wind speed from three stations in Central Anatolian Region of Turkey were utilized as input to the applied models. The input data set for modeling the ET₀ was divided to several subsets to calibrate the local data using a local modeling-based ANFIS. The estimates obtained from subset ANFIS models were compared with those of the M5 model tree (M5Tree), ANFIS models and ANN. Mean absolute error (MAE), root mean square error (RMSE), and model efficiency factor criteria were applied for analysis of models. The accuracy of M5Tree (from 15.3% to 32.5% in RMSE, from 14.4% to 24.2% in MAE), ANN (from 24.3% to 65.3% in RMSE, from 34.1% to 47% in MAE) and ANFIS (from 17.4% to 35.4% in RMSE, from 10.8% to 28.3% in MAE) models was significantly increased using subset ANFIS for estimating da ily ET_0.     

Evaluation of Class A Pan Coefficient Models for Estimation of Reference Crop Evapotranspiration in Cold Semi-Arid and Warm Arid Climates

Evapotranspiration and evaporation measurements are important parameters for many agricultural activities such as water resource management and environmental studies. There are several models which can determine pan coefficient (K _Pan), using wind speed, relative humidity and fetch length conditions. This paper analyses seven exiting pan models to estimate K _Pan values for two different climates of Iran. Monthly mean reference crop evapotranspiration (ET₀) was calculated according to the pan-ET₀ model. The results showed that estimated pan coefficients by majority of the suggested models were not statistically accurate to be used in the pan-ET₀ conversion method. However, for the cold semi-arid climate condition, the best K _Pan models for estimation of ET₀ were Orang and Raghuwanshi–Wallender, respectively. Also, the Snyder and Orang models were best fitted models for warm arid climate, respectively. The mean annual value of K _Pan, determined by Penman–Monteith FAO 56 (PMF-56) standard model for warm arid sites, was approximately 32% higher than the corresponding value in the cold semi-arid climate. Similarly, the mean annual ET₀ in the warm arid sites was 66% higher, compared to the ET₀ of the cold semi-arid sites. These types of warm arid and semi-arid climates are found widely throughout the world.     

Comparison of M5 Model Tree and Artificial Neural Network’s Methodologies in Modelling Daily Reference Evapotranspiration from NOAA Satellite Images

The objective of this study was to compare feed-forward artificial neural network (ANN) and M5 model tree for estimating reference evapotranspiration (ET₀) only on the basis of the remote sensing based surface temperature (T_s) data. The input variables for these models were the daytime surface temperature at the cold pixel obtained from the AVHRR/NOAA sensor and extraterrestrial radiation (R_a). The study has been carried out in five irrigated units that cultivate sugar cane, which located in the Khuzestan plain in the southwest of Iran. A total of 663 images of NOAA–AVHRR level 1b during the period 1999–2009, covering the area of this study were collected from the Satellite Active Archive of NOAA. The FAO-56 Penman–Monteith model was used as a reference model for assessing the performance of the two above approaches. The study demonstrated that modelling of ET₀ through the use of M5 model tree gave better estimates than the ANN technique. However, differences with the ANN model are small. Root mean square error and R² for the comparison between reference and estimated ET₀ for the tested data set using the proposed M5 model are 13.7 % and 0.96, respectively. For the ANN model these values are 14.3 % and 0.95, respectively.     

A Non-Stationary Reconnaissance Drought Index (NRDI) for Drought Monitoring in a Changing Climate

Traditionally, drought indices are calculated under stationary condition, the assumption that is not true in a changing environment. Under non-stationary conditions, it is assumed the probability distribution parameters vary linearly/non-linearly with time or other covariates. In this study, using the GAMLSS algorithm, a time-varying location parameter of lognormal distribution fitted to the initial values (α₀) of the traditional Reconnaissance Drought Index (RDI) was developed to establish a new index called the Non-Stationary RDI (NRDI), simplifying drought monitoring under non-stationarity. The fifteen meteorological stations having the longest records (1951–2014) in Iran were chose to evaluate the NRDI performances for drought monitoring. Trend analysis of the α₀ series at multiple time windows was tested by using the Mann-Kendall statistics. Although all stations detected decreasing trend in the α₀ series, eight of them were significant at the 5% probability level. The results showed that the time-dependent relationship is adequate to model the location parameter at the stations with the significant temporal trend. There were remarkable differences between the NRDI and the RDI, especially for the time windows larger than 6 months, implying monitoring droughts using the NRDI under non-stationarity. The study suggests using the NRDI where the significant time trend appears in the initial values of RDI due to changing climate.     

Reference Evapotranspiration Prediction Using Neural Networks and Optimum Time Lags

The reference evapotranspiration (ET₀) plays a significant role especially in agricultural water management and water resources planning for irrigation. It can be calculated using different empirical equations and forecasted by applying various artificial intelligence techniques. The simulation result of a machine learning technique is a function of its structure and model inputs. The purpose of this study is to investigate the effect of using the optimum set of time lags for model inputs on the prediction accuracy of monthly ET₀ using an artificial neural network (ANN). For this, the weather data time-series i.e. minimum and maximum air temperatures, vapour pressure, sunshine hours, and wind speed were collected from six meteorological stations in Serbia for the period 1980–2010. Three ANN models were applied to monthly ET₀ time-series to study the impacts of using the optimum time lags for input time-series on the performance of ANN model. Achieved results of goodness–of–fit statistics approved the results obtained by scatterplots of testing sets - using more time lags that are selected based on their correlation to the dataset is more efficient for monthly ET₀ prediction. It was realized that all the developed models showed the best performances at Loznica and Vranje stations and the worst performances at Nis station. Simultaneous assessment of the impact of using a different number of time lags and the set of time lags that show a stronger correlation to the dataset for input time-series, on the performance of ANN model in monthly ET₀ prediction in Serbia is the novelty of this study.

     

Spatial and Time Variability of Drought Based on SPI and RDI with Various Time Scales

The spatial and temporal variability of droughts were studied for the Northeast Algeria using SPI and RDI computed with monthly precipitation data from 123 rainfall stations and CFSR reanalysis monthly temperature data covering the period 1979–80 to 2013–14. The gridded temperature data was interpolated to all the locations having precipitation data, thus providing to compute SPI and RDI with the time scales of 3-, 6- and 12-month with the same observed rainfall data. Spatial and temporal patterns of droughts were obtained using Principal Component Analysis in S-Mode with Varimax rotation applied to both SPI and RDI. For all time scales of both indices, two principal components were retained identifying two sub-regions that are similar and coherent for all SPI and RDI time scales. Both components explained more than 70% and 74% of drought spatial variability of SPI and RDI, respectively. The identified sub-regions are similar and coherent for all SPI and RDI time scales. The Modified Mann-Kendall test was used to assess trends of the RPC scores, which have shown non-significant trends for decreasing drought occurrence and severity in both identified drought sub-regions and all time scales. Both indices have shown a coherent and similar behavior, however with RDI likely showing to identify more severe and moderate droughts in the southern and more arid sub-region which may be due to its ability to consider influences of global warming. Results for RDI are quite uniform relative to time scales and show smaller differences among the various climates when compared with SPI. Further assessments covering the NW and NE of Algeria using longer time series should be performed to better understand the behavior of both indices.     

Evaluation of Reference Evapotranspiration Equations Under Humid Conditions

Five reference evapotranspiration (ET₀) equations are evaluated using data from seven humid locations. The equations evaluated include Hargreaves, Thornthwaite, Turc, Priestley–Taylor, and Jensen–Haise. The objective of this study is to evaluate ET₀ estimated by these equations against the corresponding values estimated using the standardized FAO-56 Penman–Monteith (PM) equation. For each location, ET₀ estimates by the all equations were statistically compared with FAO-56 PM ET₀ estimates. The Turc equation yielded the smallest root-mean-square-difference (RMSD) values at the all locations except Novi Sad, Serbia. The final ranking of equations was based on the weighted RMSD. The Turc equation has the lowest weighted RMSD and ranking first, and other equations ranked in decreasing order are: Priestley–Taylor, Jensen–Haise, Thornthwaite, and Hargreaves. The Turc equation gives the reliable calculation at all humid locations and it has proven to be the most adjustable to the local climatic conditions. The results obtained from this study, indicate very clearly that the Turc equation is most suitable for estimating reference evapotranspiration at humid locations when weather data are insufficient to apply the FAO-56 PM equation.     

Comparison of Two Different Adaptive Neuro-Fuzzy Inference Systems in Modelling Daily Reference Evapotranspiration

This study compares two different adaptive neuro-fuzzy inference systems, adaptive neuro-fuzzy inference system (ANFIS) with grid partition (GP) method and ANFIS with subtractive clustering (SC) method, in modeling daily reference evapotranspiration (ET ₀ ). Daily climatic data including air temperature, solar radiation, relative humidity and wind speed from Adana Station, Turkey were used as inputs to the fuzzy models to estimate daily ET ₀ values obtained using FAO 56 Penman Monteith (PM) method. In the first part of the study, the effect of each climatic variable on FAO 56 PM ET ₀ was investigated by using fuzzy models. Wind speed was found to be the most effective variable in modeling ET ₀ . In the second part of the study, the effect of missing data on training, validation and test accuracy of the neuro-fuzzy models was examined. It was found that the ANFIS-GP model was not affected by missing data while the test accuracy of the ANFIS-SC model slightly decreases by increasing missing data’s percent. In the third part of the study, the effect of training data length on training, validation and test accuracy of the ANFIS models was investigated. It was found that training data length did not significantly affect the accuracy of ANFIS models in modeling daily ET ₀ . ANFIS-SC model was found to be more sensitive to the training data length than the ANFIS-GP model. In the fourth part of the study, both ANFIS models were compared with the following empirical models and their calibrated versions; Valiantzas’ equations, Turc, Hargreaves and Ritchie. Comparison results indicated that the three-and four-input ANFIS models performed better than the corresponding empirical equations in modeling ET ₀ while the calibrated two-parameter Ritchie and Valiantzas’ equations were found to be better than the two-input ANFIS models.