Spatial predictions of PAWC, DUL and CLL for grain-growing regions of NSW, Australia, from Padarian Campusano pedotransfer functions and NSW OEH datasets

Spatial predictions of plant available water capacity (PAWC), drained upper limit (DUL) and crop lower limit (CLL) for grain-growing regions of NSW, Australia, from Padarian Campusano pedotransfer functions and NSW Office of Environment and Heritage (NSW OEH) datasets.\n\nPAWC is the amount of water a soil can hold against gravity (i.e. water which does not freely drain) that is available to plants through their roots. This soil property is very important in dryland cropping areas which rely on rainfall. The maximum amount of water which can be held by a soil against gravity is called the DUL. The water that remains in a soil after plants have extracted all that is available to them is called the CLL. PAWC is calculated as DUL minus CLL.\n\nDigital soil mapping (DSM) allows the spatial prediction of soil properties across large areas using modelling techniques which combine point data measured in the field and continuous datasets related to soil forming processes such as climate, topography, land cover, existing soil mapping and lithology. Pedotransfer functions (PTFs) are equations which use the easier to measure soil attributes, e.g. sand, clay, bulk density, to model the harder to measure attributes like DUL and CLL. DSM techniques such as Latin Hypercube (LHC) sampling can be used to incorporate the uncertainties associated with the input datasets in the modelling, and to produce estimates of model output precision and reliability.\n\nThis data collection consists of spatially predicted PAWC, DUL and CLL for the grain-growing regions of New South Wales, Australia, as defined by the boundary of the Grains Research and Development Corporation's Northern Region. PAWC was modelled using PTFs for DUL and CLL from Padarian Campusano, with LHC sampling to incorporate the uncertainties associated with the input datasets.\nThe PAWC, DUL and CLL were modelled at the six Global Soil Map depths of 0-5 cm, 5-15 cm, 15-30 cm, 30-60 cm, 60-100 cm, and 100-200 cm. The top five depths have been aggregated to create a PAWC prediction for 0-100 cm.\n\nLineage: INPUT DATASETS\n1.\tSoil attribute layers from the NSW OEH via the eSpade website: clay (%), sand (%), and effective cation exchange capacity (CEC; cmol/kg). The estimated value (mean) and the RMSE values were used for all six Global Soil Map depths (0-5 cm, 5-15 cm, 15-30 cm, 30-60 cm, 60-100 cm, and 100-200 cm). https://www.environment.nsw.gov.au/eSpade2Webapp\n2.\tThe Northern Region boundary from the Grains Research and Development Corporation (GRDC)\n\nPEDOTRANSFER FUNCTIONS\nDUL and CLL equations from Padarian Campusano (2014), which used a subset of 806 soil profiles from the APSoil database that included field measurements of DUL and CLL:\n1.\tDUL = 0.2358 + 0.002572*CEC + 0.001001*clay – 1.70 x 10^-7*sand^3\n2.\tCLL = 0.6151*DUL – 0.02192\n3.\tPAWC = DUL – CLL\n\nMETHODS\nThese methods are available from Austin et al. (2019), see Related Links section.\n\nThe NSW OEH input datasets were clipped to the study area boundary and divided into tiles of 200 x 200 grid cells prior to parallel processing in a supercomputer environment. Except for the LHC sampling and correlation matrices, all code was written in Python. Layer thickness for each of the six soil depths was calculated in mm from the depth layer upper and lower bounds (e.g. 5 to 15 cm).\n\nA correlation matrix was generated in the R package for the NSW OEH clay, sand, and CEC input datasets for each of the six depths, with correlation values derived using data for the whole study area for each of the inputs.\n\nEach of the six soil depth layers was modelled separately. For every grid cell in each depth layer, the following steps were used to calculate DUL, CLL and PAWC:\n1.\tThe RMSE values for the clay, sand, and CEC input variables were used as approximations of standard deviation (SD) for input to the LHC sampling\n\n2.\tLHC sampling with a correlation matrix (from the R pse library; Chalom and Prado, 2014), using means, SDs and a correlation matrix as inputs, produced fifty realisations of each input variable. Fifty realisations were chosen following the work of Malone et al. (2015) who found that there was little difference in outcome when using more than 50 samples\n\n3.\t50 DUL and CLL values were calculated from the 50 input variable realisations using the DUL and CLL equations from Padarian Campusano (2014)\n\n4.\t50 PAWC values were calculated from the DUL and CLL values, constrained by the depth layer thickness, with units of mm\n\n5.\tFrom the 50 DUL, CLL and PAWC values for each grid cell, the mean, median, 5th and 95th percentiles, and SD were calculated and written to file as geotiffs\n\nThe tiled outputs were merged to form single rasters of the study area for DUL, CLL and PAWC at each of the six depths. Additionally, the 0-5, 5-15, 15-30, 30-60 and 60-100 cm soil depth layers were used to calculate 0-1 m versions of DUL, CLL and PAWC. The mean, median, 5th and 95th percentile values were summed to produce the 0-1 m DUL, CLL or PAWC prediction for each grid cell. This aggregation of depths assumes high correlation between layers – for example, the 95th percentile for the 0 – 1 m layer is the sum of the 95th percentiles for each contributing layer. If the layers were uncorrelated, the 95th percentile would end up closer to the mean. The SD for each of the 0-1 m DUL, CLL and PAWC layers was calculated from the summed 5th and 95th percentiles, as per the equation from Malone et al. (2011).

澳大利亚新南威尔士州（New South Wales, NSW）谷物种植区的植物有效持水量（plant available water capacity, PAWC）、排水上限（drained upper limit, DUL）与作物下限（crop lower limit, CLL）空间预测数据集，基于Padarian Campusano土壤传递函数与新南威尔士州环境与遗产办公室（NSW Office of Environment and Heritage, NSW OEH）数据集构建。

植物有效持水量（PAWC）指土壤克服重力所能持留的水量（即不会自由下渗的水分），可供植物根系吸收利用。该土壤属性在依赖降雨的旱地种植区中至关重要。土壤克服重力所能持留的最大水量称为排水上限（DUL）；植物吸收全部有效水分后残留在土壤中的水量则称为作物下限（CLL）。PAWC的计算公式为DUL减去CLL。

数字土壤制图（Digital Soil Mapping, DSM）通过结合野外实测点数据与气候、地形、土地覆被、现有土壤图、岩性等与土壤形成过程相关的连续数据集，借助建模技术实现大尺度区域土壤属性的空间预测。土壤传递函数（pedotransfer function, PTF）是一类经验方程，可通过易于测定的土壤属性（如砂粒、粘粒含量与容重），建模得到难以直接测定的DUL与CLL等属性。诸如拉丁超立方（Latin Hypercube, LHC）采样的数字土壤制图技术，可在建模过程中纳入输入数据集的不确定性，并生成模型输出精度与可靠性的估算结果。

本数据集包含澳大利亚新南威尔士州谷物种植区（以谷物研究与发展公司北部区域边界划定）的PAWC、DUL与CLL空间预测结果。PAWC通过Padarian Campusano提出的DUL与CLL土壤传递函数建模得到，并采用LHC采样纳入输入数据集的不确定性。

本次建模针对全球土壤图规定的6个土层深度：0-5 cm、5-15 cm、15-30 cm、30-60 cm、60-100 cm与100-200 cm。将前5个土层的结果进行聚合，得到0-100 cm深度的PAWC预测结果。

数据溯源：
输入数据集
1. 通过eSpade网站获取的新南威尔士州环境与遗产办公室（NSW OEH）土壤属性图层：包括粘粒（%）、砂粒（%）与有效阳离子交换量（effective cation exchange capacity, CEC；单位：cmol/kg）。针对6个全球土壤图土层深度，均采用估算值（均值）与均方根误差（root mean square error, RMSE）。相关链接：https://www.environment.nsw.gov.au/eSpade2Webapp
2. 谷物研究与发展公司（Grains Research and Development Corporation, GRDC）提供的北部区域边界矢量

土壤传递函数
Padarian Campusano（2014）提出的DUL与CLL方程，其基于APSoil数据库中包含DUL与CLL野外实测数据的806个土壤剖面子集构建，具体公式如下：
1. DUL = 0.2358 + 0.002572×CEC + 0.001001×粘粒 – 1.70×10^-7×砂粒³
2. CLL = 0.6151×DUL – 0.02192
3. PAWC = DUL – CLL

研究方法
相关方法详见Austin等人（2019）的研究成果，参见「相关链接」章节。

将NSW OEH提供的输入数据集裁剪至研究区域边界，并划分为200×200网格单元的瓦片，以在超级计算机环境中开展并行计算。除LHC采样与相关矩阵计算外，所有代码均基于Python编写。6个土层的厚度（单位：mm）根据土层上下限深度计算得到（例如5-15 cm土层厚度为100 mm）。

针对6个土层的NSW OEH粘粒、砂粒与CEC输入数据集，通过R语言包生成相关矩阵，相关系数基于全研究区域的输入数据计算得到。

6个土层分别独立建模。针对每个土层的所有网格单元，采用以下步骤计算DUL、CLL与PAWC：
1. 将粘粒、砂粒与CEC输入变量的RMSE值作为标准差（standard deviation, SD）的近似值，用于LHC采样的输入参数
2. 基于R语言pse包（Chalom与Prado，2014）生成的相关矩阵，以均值、标准差与相关矩阵为输入，通过LHC采样为每个输入变量生成50个实现样本。参考Malone等人（2015）的研究成果，选择50个实现样本即可满足精度要求，增加样本数量对结果影响极小
3. 基于Padarian Campusano（2014）的DUL与CLL公式，由50个输入变量实现样本计算得到50组DUL与CLL值
4. 由50组DUL与CLL值计算得到50组PAWC值，结果受土层厚度约束，单位为mm
5. 针对每个网格单元的50组DUL、CLL与PAWC值，计算其均值、中位数、5%与95%分位数以及标准差，并以GeoTIFF格式写入文件

将所有瓦片输出结果进行拼接，得到6个土层深度下覆盖全研究区域的DUL、CLL与PAWC单波段栅格。此外，利用0-5 cm、5-15 cm、15-30 cm、30-60 cm与60-100 cm这5个土层的结果，计算得到0-1 m深度的DUL、CLL与PAWC预测值。针对每个网格单元，将各土层的均值、中位数、5%与95%分位数分别求和，得到0-1 m深度的对应预测值。该土层聚合方法假设各土层间存在高度相关性——例如，0-1 m土层的95%分位数为各参与土层95%分位数的和。若土层间互不相关，则95%分位数会更接近均值。参考Malone等人（2011）的公式，由求和得到的5%与95%分位数计算得到0-1 m深度DUL、CLL与PAWC图层的标准差。