以坡位为空间配置单元的流域管理措施情景优化方法

基于流域过程模型的BMP情景分析是当前流域管理措施评价、非点源污染控制等研究应用中广泛采用的方法,但其通常采用的BMP空间配置单元（地块、农场、水文响应单元或子流域）与坡面上的地形部位关系较弱,难以有效地根据坡面过程特点表达坡面上多种BMP之间的空间配置关系,影响了BMP情景优化效率和结果的合理性。为此,本文提出以坡位单元作为BMP空间配置单元,将各种BMP在不同坡位间合理的空间配置关系显式表达为基于坡位的空间配置规则,通过结合NSGA-II优化算法建立了一套基于坡位单元的BMP空间配置优化方法。应用案例表明,本文构建的基于坡位单元的BMP情景优化方法可有效利用基于坡位的空间配置规则进行BMP情景优化,优化所得的BMP空间配置方案更为合理,优化效率较高。     

Modelling the Effects of Land-use Change on Runoff and Sediment Yield in the Weicheng River Watershed,Southwest China

As a major sediment area in the upper Yangtze River, Jialing River basin experienced substantial land-use changes, many water conservancy projects were constructed from the 1980 s onward to promote water and soil conservation. The water and sediment yield at the watershed outlet was strongly affected by these water conservation works, including ponds and reservoirs, which should be considered in the modelling. In this study, based on the observed data of the Weicheng River catchment, the relationships between precipitation, runoff, vegetation, topography and sediment yield were analyzed, a distributed runoff and sediment yield model(WSTD-SED) was developed, and the hydrological processes of different land-use scenarios were simulated by using the model. The main results are summarized as follows: 1) there is an alternating characteristic in river channels and reservoirs in the Jialing River hilly area, with scour occurring in wet years and deposit occurring in dry years. 2) Most of the sediment deposited in river channels and reservoirs is carried off by the largest flood in the year. 3) The model yielded plausible results for runoff and sediment yield dynamics without the need of calibration, and the WSTD-SED model could be usedto obtain qualitative estimates on the effects of land use change scenarios. 4) The modelling results suggest that a 10% increase in cropland(dry land) reforestation results in a 0.7% decrease in runoff and 1.5% decrease in sediment yield.     

SWAT模型对高精度土壤信息的敏感性研究

土壤信息是SWAT模型的重要输入数据,通常认为,土壤信息的精度直接影响着模拟结果的准确性。本文以美国Brewery Creek流域(19.5km²)为例,在其他输入不变的情况下,通过比较不同精度土壤数据(美国农业部SSURGO土壤图与SoLIM方法获得的土壤图)的模拟径流,分析SWAT模型对高精度土壤信息的敏感性。应用结果显示,在模型的校正前后,两种土壤数据的径流模拟结果均近似,差别并不显著。这表明在小流域水文模拟中,SWAT模型的径流模拟对高精度土壤信息的敏感性较弱,模拟径流不能很好的体现一定精度基础上土壤信息的差别。本文将此现象主要归因于:SWAT模型所采用的SCS-CN径流计算方法,在计算CN值(Curve Number)时将不同土壤类型综合到四个土壤水文组的做法,概括了土壤信息,模糊了土壤之间的属性差别,损失了土壤精度信息。本研究发现了SCS-CN径流计算方法在利用高精度土壤数据时存在的问题,并进行了分析,为水文模拟中参数的确定和数据的准备提供了参考。     

黑河山区流域平均坡长的计算与径流模拟

 流域平均坡长是侧向流和汇流时间计算的重要参数,其会影响地表径流的计算。应用SWAT 2005和ArcView GIS 3.2集成的AVSWAT模型,对黑河干流上游山区流域莺落峡出山口径流进行模拟,发现其计算的流域平均坡长存在较大误差,进而影响到模拟结果。利用子流域内已知的平均坡度和平均坡长建立回归方程,计算各子流域的平均坡长,替换AVSWAT计算的不合理值,在保持其他参数不变的情况下,模拟的月径流纳什系数从0.60提高到0.75,模拟结果得到显著提高。敏感性分析结果和径流曲线数(CN2)的分析也间接验证了流域平均坡长修正方法的可行性。在修正流域平均坡长后,对AVSWAT模型的其他参数CN2等进行优化,模拟的月径流的纳什系数达到0.81,表明本文建议的流域平均坡长计算方法是可以应用到实际的干旱区黑河流域并取得较好模拟效果。     

Daily and Monthly Suspended Sediment Load Predictions Using Wavelet Based Artificial Intelligence Approaches

In the current study, the efficiency of Wavelet-based Least Square Support Vector Machine(WLSSVM) model was examined for prediction of daily and monthly Suspended Sediment Load(SSL) of the Mississippi River. For this purpose, in the first step, SSL was predicted via ad hoc LSSVM and Artificial Neural Network(ANN) models; then,streamflow and SSL data were decomposed into subsignals via wavelet, and these decomposed sub-time series were imposed to LSSVM and ANN to simulate discharge-SSL relationship. Finally, the ability of WLSSVM was compared with other models in multistep-ahead SSL predictions. The results showed that in daily SSL prediction, LSSVM has better outcomes with Determination Coefficient(DC)=0.92 than ad hoc ANN with DC=0.88. However unlike daily SSL, in monthly modeling, ANN has a bit accurate upshot.WLSSVM and wavelet-based ANN(WANN) models showed same consequences in daily and different in monthly SSL predictions, and adding wavelet led to more accuracy of LSSVM and ANN. Furthermore,conjunction of wavelet to LSSVM and ANN evaluated via multi-step-ahead SSL predictions and, e.g.,DC LSSVM=0.4 was increased to the DC WLSSVM=0.71 in 7-day ahead SSL prediction. In addition, WLSSVM outperformed WANN by increment of time horizon prediction.     

Projection of future streamflow of the Hunza River Basin,Karakoram Range (Pakistan) using HBV hydrological model

Hydrologiska Byrans Vattenbalansavdeling(HBV) Light model was used to evaluate the performance of the model in response to climate change in the snowy and glaciated catchment area of Hunza River Basin. The study aimed to understand the temporal variation of streamflow of Hunza River and its contribution to Indus River System(IRS). HBV model performed fairly well both during calibration(R2=0.87, Reff=0.85, PBIAS=-0.36) and validation(R2=0.86, Reff=0.83, PBIAS=-13.58) periods on daily time scale in the Hunza River Basin. Model performed better on monthly time scale with slightly underestimated low flows period during bothcalibration(R2=0.94, Reff=0.88, PBIAS=0.47) and validation(R2=0.92, Reff=0.85, PBIAS=15.83) periods. Simulated streamflow analysis from 1995-2010 unveiled that the average percentage contribution of snow, rain and glacier melt to the streamflow of Hunza River is about 16.5%, 19.4% and 64% respectively. In addition, the HBV-Light model performance was also evaluated for prediction of future streamflow in the Hunza River using future projected data of three General Circulation Model(GCMs) i.e. BCC-CSM1.1, CanESM2, and MIROCESM under RCP2.6, 4.5 and 8.5 and predictions were made over three time periods, 2010-2039, 2040-2069 and 2070-2099, using 1980-2010 as the control period. Overall projected climate results reveal that temperature and precipitation are the most sensitiveparameters to the streamflow of Hunza River. MIROC-ESM predicted the highest increase in the future streamflow of the Hunza River due to increase in temperature and precipitation under RCP4.5 and 8.5 scenarios from 2010-2099 while predicted slight increase in the streamflow under RCP2.6 during the start and end of the 21 th century. However, BCCCSM1.1 predicted decrease in the streamflow under RCP8.5 due to decrease in temperature and precipitation from 2010-2099. However, Can ESM2 predicted 22%-88% increase in the streamflow under RCP4.5 from 2010-2099. The results of this study could be useful for decision making and effective future strategic plans for water management and their sustainability in the region.     

Modeling regional landslide susceptibility using dynamic soil moisture profiles

A landslide susceptibility mapping study was performed using dynamic hillslope hydrology. The modified infinite slope stability model that directly includes vadose zone soil moisture (SM) was applied at Cleveland Corral, California, US and Krishnabhir, Dhading, Nepal. The variable infiltration capacity (VIC-3L) model simulated vadose zone soil moisture and the wetness index hydrologic model simulated groundwater (GW). The GW model predictions had a 75% NASH-Sutcliffe efficiency when compared to California’s in-situ GW measurements. The model performed best during the wet season. Using predicted GW and VIC-3L vadose zone SM, the developed landslide susceptibility maps showed very good agreement with mapped landslides at each study region. Previous quasi-dynamic model predictions of Nepal’s hazardous areas during extreme rainfall events were enhanced to improve the spatial characterization and provide the timing of hazardous conditions.     

Evaluating Suitability of Multiple Precipitation Products for the Lancang River Basin

Global reanalysis precipitation products could provide valuable meteorological information for flow forecasting in poorly gauged areas, helping to overcome a long-standing challenge in the field. But not all data sources are suitable for all regions or perform the same way in hydrological modeling, so it is essential to test the suitability of precipitation products before applying them. In this study, five widely used global high-resolution precipitation products—Asian Precipitation Highly Resolved Observational Data Integration Towards Evaluation of Water Resources(APHRODITE), National Centers for Environmental Prediction Climate Forecast System Reanalysis(NCEP-CFSR), Climate Hazards Group InfraRed Precipitation with Station Data(CHIRPS), China Gauge-based Daily Precipitation Analysis developed by China Meteorological Administration(CMA) and Agricultural Model Intercomparison and Improvement Project based on the NASA Modern-Era Retrospective Analysis for Research and Applications(AgMERRA)—were evaluated using statistical methods and a hydrological approach for their suitability for the Lancang River Basin. The results indicated that APHRODITE, CMA, AgMERRA and CHIRPS were more accurate precipitation indicators than NCEP-CFSR in terms of the multiyear average and seasonal spatial distribution pattern, all of the CHIRPS, Ag MERRA and APHRODITE perform better than CMA and NCEP-CFSR at the small, medium and high precipitation intensities ranges in subbasin11 and sunbabsin46. All five products performed better in subbasin46(a low-altitude region) than in subbasin11(a high-altitude region) on the daily and monthly scales. In addition to NCEP-CFSR, the other four products all presented encouraging potential for streamflow simulation at daily(Yunjinghong) and monthly(Yunjinghong, Jiuzhou and Gajiu) scale. Hydrological simulations forced with APHRODITE were the best of the five for the Yunjinghong station in capturing daily and monthly measured streamflow. Except for NCEP-CFSR, all products were very good for hydrological simulations for the Gajiu and Jiuzhou stations.     

Application of land-use change model in guiding regional planning: A case study in Hun-Taizi River Watershed,Northeast China

This paper firstly investigated the land-use and land-cover change (LUCC) in the Hun-Taizi River watershed, Northeast China from 1988 to 2004 based on remotely sensed images and geographic information systems (GIS) technology. Then, using the famous land-use change model of Conversion of Land Use and its Effects at Small regional extent (CLUE-S), this paper simulated the land use changes under historical trend (HT), urban planning (UP) and ecological protection (EP) scenarios considering urban planning and ...     

基于坡位-地块单元的流域最佳管理措施空间优化配置方法

最佳管理措施（BMP）是治理流域土壤侵蚀、非点源污染等环境问题的有效途径,基于流域过程模拟的情景优化方法可得到综合效益近似最优的BMP空间配置方案集。目前用于配置BMP的空间单元（如子流域、水文响应单元、地块、坡位）均不能有效地综合体现BMP与地形部位间的空间关系以及同一地形部位内不同土地利用斑块上的BMP差异。本文提出将坡位单元与地块单元叠加生成的坡位-地块单元作为BMP空间配置单元,结合分布式流域建模框架SEIMS和多目标优化算法NSGA-II建立一套流域BMP空间优化配置方法。以江苏省溧阳市中田舍流域的非点源污染治理为例,选取减量施肥、退耕还林、封山育林和生态林草4种典型BMP,以最大化总氮削减率、最小化经济成本为优化目标,分别采用坡位单元、地块单元、坡位-地块单元进行情景优化。结果表明：相比坡位单元和地块单元,采用坡位-地块单元可获得最多具有近似最优综合效益的BMP情景,定量评价解集分布性和收敛性的Hypervolume指数分别提升了7%和4%,且BMP在空间上分布更加精细、配置更加灵活。本文方法可有效、合理地优化流域最佳管理措施的空间配置,为流域治理提供决策支持。     

Spatial analysis of the impact of land-use on surface runoff and soil erosion-a case study of western Jilin

The impact of land-use on surface runoff and soil erosion is still poorly understood at basin scale. Thus in the Western Jilin Ecosystem (WJE), surface runoff and soil erosion were measured against identified land-use types in the basin. Due to the spatial nature of the analysis, GIS ArcMap version 9.1 and the WetSpass model were used in the simulation process. In the study, the WetSpass model was extended with the Dynamic Sediment Balance Equation (Ziegler et al., 1997), to simulate and quantify soil erosion. A hypothetical natural grassland scenario was developed for the study area and compared with the present land-use management conditions. The results indicate significant differences in runoff and soil erosion across the different land-use types both within and between the two scenarios. Calculated averages of surface runoff and soil erosion for the present land-use management were 48.03 mm/a and 83.43 kg/(m2·a) respectively. Those for the hypothetical natural grassland scenario were 24.70 mm/a and 78.36 kg/m2·a) . Thus an overall decrease in runoff and soil erosion was observed as the conditions changed from the present land-use management to the hypothetical natural grassland state. Under the present land-use management, urban settlements exhibited the highest surface runoff but one of the least soil erosions, while bare-lands showed the highest soil erosion. It was more generally observed that runoff and erosion varies with vegetation type/density. It was concluded based on the research findings that the present land-use management might not be the best scenario for the ecosystem as it showed increased basin runoff and soil erosion in comparison with the natural grassland vegetation. Since no best scenario was simulated for or advanced in the study, further research to develop a more balanced land management system is thus required. The findings of the study can assist in the identification of vulnerable/fragile ecosystems in the basin and to guide sustainable future planning and development of the basin.     

基于洪峰模数的山洪灾害雨量预警指标研究

山洪灾害预警是防御山洪的重要非工程措施,雨量预警指标是山洪灾害预警的关键。目前的雨量预警指标计算方法对水文气象资料条件以及模型建模率定都有很高的要求,并不适用于基层防汛人员。因此,本文基于全国山洪灾害调查评价成果数据,提出了一种运用洪峰模数计算雨量预警指标的简便、易用的方法。该方法以小流域洪水计算推理公式为基础,将公式中流量与流域面积的比值用洪峰模数表示,得到基于洪峰模数的临界雨量估算公式,并考虑流域土壤含水量等因素,分析临界雨量变化阈值,最终得到雨量预警指标。本文以云南省绥江县双河小流域为例,计算结果显示不同时段（1 h、3 h、6 h）净雨量和预警时段呈线性关系。降雨损失计算中洼地蓄水和植被截留在不同时段相同,土壤下渗在不同的时段不相同。在此基础上,计算不同土壤含水量条件下,不同时段的雨量预警指标。最后,对临界流量、降雨损失和预警指标进行了合理性分析,结果显示预警指标和调查评价结果及实测降雨都比较接近,计算的预警指标合理。本研究为基层山洪灾害预警提供了一种快速、便捷的预警指标计算方法,为预警指标计算提供技术支持。     

Analysis of long-term dependence phenomenon in Benue River flow process and its hypothesis testing

In this paper, the long-term dependence phenomenon （the Hurst Effect） which characterizes hydrological and other geophysical times series is studied. The long-term memory is analysed for both daily and monthly streamflow series of the Benue River at Makurdi, Nigeria by using heuristic methods and testing specifically the null hypothesis of short-term memory in the monthly flow series. Results obtained by applying heuristic procedures indicated that there may be the presence of long-term memory component in mean daily flow series but there is no discernible reason to suspect the presence in both average monthly and maximum monthly flow series （extreme event）. Hypothesis testing was conducted by using original and modified versions of rescaled range statistic. When the modified rescaled range, which accounts for short-term memory in the series, is used, the null hypothesis is accepted for both the average monthly and maximum monthly flow series, indicating little or no probable presence of long-term memory in the series. An identical conclusion is also arrived at when second null hypothesis for independence of the monthly flow series is tested. Therefore, apart from the mean daily flow series, there is little evidence of long-term dependence in the Benue River streamflow series at Makurdi. However, considering the limited length of data used, the results are inconclusive.     

Elevation,slope aspect and integrated nutrient management effects on crop productivity and soil quality in North-west Himalayas,India

On farm bio-resource recycling has been given greater emphasis with the introduction of conservation agriculture specifically withclimate change scenarios in the mid-hills of the north-west Himalaya region（NWHR）. Under this changing scenario, elevation, slope aspect and integrated nutrient management（INM） may affect significantly soil quality and crop productivity. A study was conducted during 2009-2010 to 2010-2011 at the Ashti watershed of NWHR in a rainfed condition to examine the influence of elevation, slope aspect and integrated nutrient management（INM） on soil resource and crop productivity. Two years of farm demonstration trials indicated that crop productivity and soil quality is significantly affected by elevation, slope aspect and INM. Results showed that wheat equivalent yield（WEY） of improved technology increased crop productivity by -20%-37% compared to the conventional system. Intercropping of maize with cowpea and soybean enhanced yield by another 8%-17%. North aspect and higher elevation increased crop productivity by 15%-25% compared to south aspect and low elevation（except paddy）. Intercropping of maize with cowpea and soybean enhanced yield by another 8%-15%. Irrespective of slope, elevation and cropping system, the WEY increased by -30% in this region due to INMtechnology. The influence of elevation, slope aspect and INM significantly affected soil resources（SQI） and soil carbon change（SCC）. SCC is significantly correlated with SQI for conventional（R2 = 0.65＊）, INM technology（R2 = 0.81＊） and for both technologies（R2 = 0.73＊）. It is recommended that at higher elevation.（except for paddy soils） with a north facing slope, INM is recommended for higher crop productivity; conservation of soil resources is recommended for the mid hills of NWHR; and single values of SCC are appropriate as a SQI for this region.     

Development of a location-weighted landscape contrast index based on the minimum hydrological response unit

The changing patterns of watersheds in a landscape, driven by human activities, play an important role in non-point source pollution processes. This paper aims to improve the location-weighted landscape contrast index using remote sensing and GIS technology to account for the effects of scale and ecological processes. The hydrological response unit(HRU) with a single land use and soil type was used as the smallest unit. The relationship between the landscape index and typical ecological processes was established by describing the influence of the landscape pattern on non-point source pollution. To verify the research method, this paper used the Yanshi River basin as a study area. The results showed that the relative intensity of non-point source pollution in different regions of the watershed and the location-weighted landscape contrast index based on the minimum HRU can qualitatively reflect the risk of regional nutrient loss.     

遥感及再分析降水产品在缺资料干旱内陆盆地的适用性评估

山区降水较集中,但降水测站多位于山谷或人口密集区,代表性差。遥感和再分析降水产品能提供时空分布连续的数据,不受地形条件限制。柴达木盆地中心属干旱荒漠区,水是制约该区开发的首要条件,其四周属高寒山区,降水相对较多,但降水监测十分薄弱。为获取该区相对精确的降水时空分布信息,本文评估了4套高分辨率降水产品（CMADS、TRMM、GPM和MSWEP）的适用性。首先基于地面站点数据评估它们在不同时空尺度上的精度,并分析它们在柴达木盆地的空间分布和年内分配特征。然后,以盆地东南隅的无测站山区香日德河流域为研究区,利用降水产品驱动SWAT模型来评估它们的分布式水文模拟适用性。结果表明：(1) MSWEP在年、月尺度上与站点降水的吻合程度最高（R≥0.79,PBIAS=0.5%）,其次是GPM和TRMM,CMADS精度最低（R≥0.64,PBIAS=5.8%）;(2)从降水精度与站点高程的关系来看,降水产品在相对低海拔区容易高估站点降水,而在相对高海拔区常低估实际降水;(3)在香日德河流域,MSWEP(NSE=0.64)在基准期（2009—2012年）的径流模拟表现明显好于其它降水产品（NSE=0.3...     

基于SWAT模型和多源DEM数据的流域水系提取精度分析

流域水系是研究水文水资源、地貌演化和生态环境及水土治理等的基础数据,高精度的水系提取对流域研究十分重要。本文以空间分辨率均为30 m的 AW3D30 DSM、SRTM1 DEM和ASTER GDEM2数字高程模型作为基本的地形数据,基于SWAT模型提取犟河流域水系,通过河网“套合差”、水系相对误差、Google Map水文数据及蓝线河网对提取结果进行误差分析与综合评价,探讨河道剖面和地形特征对水系提取精度的影响。结果表明：① 集水面积阈值是决定河网水系提取精度的关键参数,阈值越大,提取的河网密度越小,反之提取的河网密度越大;② 基于河网密度与集水阈值二阶导数的幂函数与直线相切的数学求值方法确定流域最佳集水面积阈值,能避免最佳集水阈值取值的主观性,提取的河网水系与实际河道相符;③ AW3D30 DSM数据提取的流域河网水系与Google Map高分辨率影像的水系偏差最小,且AW3D30 DSM数据提取的水系与蓝线河网的河网“套合差”和水系相对误差值均最低,能真实反映中低山丘陵山区流域水系发育的疏密程度,吻合度最好;④ 多源DEM数据提取结果均显示为河床比降大和横剖面曲线为窄深式的“V”形河谷提取的水系精度高于河床比降小和横剖面曲线为 “碟”形河谷的提取精度;⑤ AW3D30 DSM数据的地形起伏和坡度标准差最大,有利于山区河网水系的提取。因此,基于SWAT模型和AW3D30 DSM数据提取的山区流域水系可最大限度反映流域水系的真实情况,精度最高,此方法和数据源可应用于中低山丘陵山区流域的水系提取研究。     

A Participatory GIS Approach to Identify Critical Land Degradation Areas and Prioritize Soil Conservation for Mountainous Olive Groves （Case Study）

Climate change scenarios predict an increase in the frequency of heavy rainfall events in some areas. This will increase runoff and soil erosion, and reduce agricultural productivity, particularly on vulnerable mountainous agricultural lands that is already exhibiting high rates of soil erosion. Haphazard implementation of soil and water conservation （SWC） interventions on scattered fields is inefficient in reducing soil erosion. The objective of this study was to identify areas at high risk of erosion to aid the design and implementation of sustainable SWC using GIS analysis and farmers＇ participation approach. A 25 m digital elevation model （DEM） was used to derive layers of flow accumulation, slope steepness and land curvature, which were used to derive an erosion-risk （priority） map for the whole watershed. Boundaries of farmers＇ fields were mapped and verified by the community and each field was classified into high, moderate or low erosion risk. Fields with low flow accumulation （top of hill） and/or steep slope and/or convex slope were assigned high erosion risk and therefore high implementation priority. The study showed that more than 54% of the fields were classified into high erosion risk areas. Accordingly, a community-watershed plan was established, revised and approved by the community.Incentive loans to implement SWC measures were distributed to 100 farmers based on the priorities of their fields. Judged by local farmers and using 16 randomly selected fields, 90% of the targeted areas were correctly identified using the erosion risk map. After two years, the conservation measures had led to marked improvement of soil conservation. The approach is simple and easy to comprehend by the community and provides scientific basis to prioritize the implementation of SWC and to target the most degraded areas, which amplify the impact of these in reducing the vulnerability to land degradation.     

TRMM及GPM降水数据在高寒内陆河流域的准确性评估

降水数据的准确性和时空分辨率成为水文过程模拟的关键.卫星遥感降水资料的日益丰富为资料缺乏区的水文模拟带来了新的突破.本研究拟在资料缺乏、下垫面复杂,观测难、建模难的柴达木盆地高寒内陆河流域—巴音河中上游,基于近5年的TMPA 3B42、GPM IMERG V5及GPM IMERG V6逐日降水数据和气象站点观测数据建立...     

Analysis of stochastic characteristics of the Benue River flow process

Stochastic characteristics of the Benue River streamflow process are examined under conditions of data austerity. The streamflow process is investigated for trend, non-stationarity and seasonality for a time period of 26 years. Results of trend analyses with Mann-Kendall test show that there is no trend in the annual mean discharges. Monthly flow series examined with seasonal Kendall test indicate the presence of positive change in the trend for some months, especially the months of August, January, and February. For the stationarity test, daily and monthly flow series appear to be stationary whereas at 1%, 5%, and 10% significant levels, the stationarity alternative hypothesis is rejected for the annual flow series. Though monthly flow appears to be stationary going by this test, because of high seasonality, it could be said to exhibit periodic stationarity based on the seasonality analysis. The following conclusions are drawn： （1） There is seasonality in both the mean and variance with unimodal distribution. （2） Days with high mean also have high variance. （3） Skewness coefficients for the months within the dry season period are greater than those of the wet season period, and seasonal autocorrelations for streamflow during dry season are generally larger than those of the wet season. Precisely, they are significantly different for most of the months. （4） The autocorrelation functions estimated ＂over time＂ are greater in the absolute value for data that have not been deseasonalised but were initially normalised by logarithmic transformation only, while autocorrelation functions for i = 1, 2 365 estimated ＂over realisations＂ have their coefficients significantly different from other coefficients.