3.1 Random forest regressor algorithm
3.1随机森林回归器算法

As the aim here is to predict a continuous numerical value for sea-surface iodide, a regression approach is taken. As discussed in the introduction, previous approaches have been made to parameterise sea-surface iodide, and the most commonly used relationships employ sea-surface temperature as the predictor variable. Here we take a different multivariate and non-parametric approach, using the computationally cheap and interpretable random forest regressor (RFR) algorithm (Breiman, 2001; Pedregosa et al., 2011).
由于此处的目的是预测海面碘化物的连续数值，因此采用回归方法。正如引言中所讨论的，之前已经采用了参数化海面碘化物的方法，最常用的关系式采用海面温度作为预测变量。在这里，我们采用不同的多变量和非参数方法，使用计算成本低且可解释的随机森林回归（RFR）算法（ Breiman ， 2001 ； Pedregosa 等人， 2011 ） 。

Random forest regression is based on finding a number of decisions trees, which predict the dependent variable. All of the trees contribute to the prediction, and they are collectively referred to as a “forest”. These trees can be explained as a record of the way the algorithm has linearly traversed a subset of the training data, splitting the data into two parts at each decision point or “node” in a way that minimised the internal differences of the parts. The best split is chosen between the available variables based on an error metric (e.g. mean square error), and this process is continued until a criterion of purity is reached or a minimum number of data points are left from a split. This is essentially a classification problem. The prediction of the forest is the mean value of the prediction of all of the different decision trees, which attempts to make the results more of a regression problem. More details of this approach can be found in Friedman et al. (2009).
随机森林回归基于查找多个决策树，这些决策树预测因变量。所有树木都对预测做出贡献，它们统称为“森林”。这些树可以解释为算法线性遍历训练数据子集的方式的记录，在每个决策点或“节点”将数据分成两部分，以最小化各部分内部差异的方式。基于误差度量（例如均方误差）在可用变量之间选择最佳分割，并且继续该过程直到达到纯度标准或分割留下最小数量的数据点。这本质上是一个分类问题。森林的预测是所有不同决策树的预测的平均值，它试图使结果更像是一个回归问题。有关此方法的更多详细信息，请参见Friedman 等人。 （ 2009 ） 。

This approach differs from previous approaches which have individually tested proposed relationships and selected the best-performing model(s) as a parameterisation (e.g. Table A1). Here, an algorithm uses the data it is provided to build a model that gives a prediction, and therefore it is the data themselves that define the model that is used to predict new values. A key difference of this approach is also that only a subset, the training set, is used to build the model, and the rest (or withheld set) is then used to test the performance of the model. Here we use 80  % of the data for the training set and use the remaining 20 % as the withheld set (also commonly referred to as the “testing set”).
该方法不同于先前的方法，先前的方法单独测试了所提出的关系并选择性能最佳的模型作为参数化（例如表A1 ）。在这里，算法使用所提供的数据来构建给出预测的模型，因此数据本身定义了用于预测新值的模型。这种方法的一个关键区别还在于，仅使用一个子集（训练集）来构建模型，然后使用其余部分（或保留集）来测试模型的性能。这里我们使用 80% 的数据作为训练集，使用剩余的 20% 作为保留集（通常也称为“测试集”）。

To ensure that the models built are generalisable and mitigate overfitting, the random forest approach used here artificially increases the randomness within the forest (Pedregosa et al., 2011). This is done by randomly combining single decision trees by an approach referred to as “bootstrap aggregation” or “bagging” (Breiman, 2001; Tong et al., 2003). This additional bagging approach randomly samples observations within the training dataset and so mitigates overfitting of the trees to the dataset (Friedman et al., 2009). Furthermore, a stratified sampling approach was taken. Specifically, the overall dataset was split into quartiles according to iodide concentration value, and training data were randomly selected from each quartile. This approach was used to maintain the same statistical distribution in the training/testing data as the overall dataset.
为了确保建立的模型具有普适性并减轻过度拟合，这里使用的随机森林方法人为地增加了森林内的随机性（ Pedregosa et al. , 2011 ） 。这是通过称为“引导聚合”或“装袋”的方法随机组合单个决策树来完成的（ Breiman ， 2001 ； Tong 等人， 2003 ） 。这种额外的装袋方法对训练数据集中的观察结果进行随机采样，从而减轻了树与数据集的过度拟合（ Friedman 等人， 2009 ） 。此外，还采取了分层抽样的方法。具体来说，根据碘化物浓度值将整个数据集分成四分位数，并从每个四分位数中随机选择训练数据。这种方法用于保持训练/测试数据与整个数据集相同的统计分布。

Machine learning algorithms can generally be tuned to increase performance using settings called hyperparameters. However, random forests are known to generally perform well without tuning. The default hyperparameters were therefore used here (Pedregosa et al., 2011), except for increasing the number of trees (“n_estimators”) from 10 to 500. Mean square error (MSE) was used as the criterion for evaluating each split (also referred to as a “node”). The maximum number of “features” (the ancillary variables provided to the algorithm, such as temperature or nitrate concentration) considered when looking for the best split is set to the number provided to the algorithm. The number of splits a tree is allowed to make (“max_depth”) is not restricted, and further nodes are made until leaves contain less than two samples (“min_samples_split”) and a minimum of one (“min_samples_leaf”). All the random forest models are built using bootstrapping.
通常可以使用称为超参数的设置来调整机器学习算法以提高性能。然而，众所周知，随机森林通常无需调整即可表现良好。因此，这里使用默认的超参数（ Pedregosa et al. ， 2011 ） ，除了将树的数量（“n_estimators”）从 10 增加到 500 之外。均方误差（MSE）被用作评估每个分割的标准（也称为“节点”）。寻找最佳分割时考虑的“特征”（提供给算法的辅助变量，例如温度或硝酸盐浓度）的最大数量设置为提供给算法的数量。允许树进行分割的数量（“max_depth”）不受限制，并且会生成更多节点，直到叶子包含少于两个样本（“min_samples_split”）且至少包含一个样本（“min_samples_leaf”）。所有随机森林模型都是使用引导构建的。

3.2 Error and uncertainty calculations
3.2误差和不确定性计算

Understanding the errors and uncertainties in the global iodide distribution is important due to any sensitivities to this value within the modelled Earth system. We consider three sources of error in our predictions: the “dataset selection” error due to the splitting of the dataset into training and withheld parts, the “model selection error” due to the choice of dependent variables, and the “observational error” on the iodide measurements.
由于模拟地球系统内对该值的敏感性，了解全球碘化物分布的误差和不确定性非常重要。我们在预测中考虑三个误差来源：由于将数据集分为训练部分和保留部分而导致的“数据集选择”误差，由于因变量的选择而导致的“模型选择误差”，以及由于变量的选择而导致的“观察误差”碘化物测量。

To quantify the range of the dataset selection error, we construct models from 20 pseudo-random splits of the dataset into training and withheld parts. The hyperparameters and input ancillary variables are kept the same for the generation of the 20 models, so that the only difference between the models is the training dataset. These 20 models are then used to predict the withheld data. Performance metrics (e.g. root mean square error (RMSE) and average absolute prediction) can then be calculated for each model. This gives a range of 20 values, which can then be converted to a percentage range as the error. This is done by dividing the largest range in predicted values for a model by the minimum predicted value, to give a maximum value for the range of error, and then taking the smallest range in the predicted values and dividing this by the maximum value, to give a minimum value for the error range. Significant differences between the model's performance metrics would suggest important sensitivity to the training/withheld dataset splits.
为了量化数据集选择误差的范围，我们将数据集的 20 个伪随机分割构建为训练部分和保留部分。生成 20 个模型时，超参数和输入辅助变量保持相同，因此模型之间的唯一区别是训练数据集。然后使用这 20 个模型来预测保留的数据。然后可以计算每个模型的性能指标（例如均方根误差（RMSE）和平均绝对预测）。这给出了 20 个值的范围，然后可以将其转换为百分比范围作为误差。这是通过将模型预测值的最大范围除以最小预测值来完成的，以给出误差范围的最大值，然后取预测值的最小范围并将其除以最大值，得到给出误差范围的最小值。模型性能指标之间的显着差异表明对训练/保留数据集分割的重要敏感性。

We define the “model selection” error as the uncertainty resulting from the choice of input ancillary variables. A number of combinations of input variables are possible in generating the models, and each will generate a different prediction. We quantify this error as the difference in performance against the withheld dataset and prediction value (e.g. average global value). Similarly to our calculation of the dataset selection error, this can be converted to percentage error by considering the range in these values and dividing them by minimum and maximum values.
我们将“模型选择”误差定义为由于选择输入辅助变量而产生的不确定性。在生成模型时可以使用多种输入变量组合，并且每种组合都会生成不同的预测。我们将此误差量化为与保留数据集和预测值（例如平均全局值）的性能差异。与我们计算数据集选择误差类似，可以通过考虑这些值的范围并将它们除以最小值和最大值来将其转换为百分比误差。

For the observational error we refer to Chance et al. (2019a), who provide individual error estimates for each of the iodide observations in the data compilation. Over half (51 %) of the data points have an error of 5 % or less, and a further ∼25 % have an uncertainty in the range of 5 %–10 %. We therefore use a value of 10 % as a conservative estimate of the observational error.
对于观察误差，我们参考Chance 等人。 ( 2019 a ) ，他们为数据汇编中的每个碘化物观测值提供了单独的误差估计。超过一半 (51%) 的数据点的误差为 5% 或更少，另外约 25 % 的数据点的不确定性在 5%–10% 范围内。因此，我们使用 10% 的值作为观测误差的保守估计。

3.3 Outlier identification and removal
3.3异常值识别和去除

Our dataset consists of values for ancillary variables and iodide concentration for all of the 1342 measurement locations in the observational dataset (Sect. 2). As discussed in Sect. 3.1, we split this dataset into two parts: (i) a training set for use in building and optimising models, and (ii) a withheld set to evaluate the models built. Particular care was taken to ensure the withheld and training datasets were representative of the entire dataset in the way the models are built, therefore improving performance and generalisability to unseen data (see Sect. 3.1).
我们的数据集由观测数据集中所有 1342 个测量位置的辅助变量值和碘化物浓度组成（第2节）。正如第 3 节中所讨论的那样。 3.1中，我们将该数据集分为两部分：（i）用于构建和优化模型的训练集，以及（ii）用于评估构建的模型的保留集。我们特别注意确保保留数据集和训练数据集以模型构建的方式代表整个数据集，从而提高性能和对未见数据的通用性（参见第3.1节）。

We take a random forest regressor model built with variables that were intuitively assumed to give a reasonable ability to differentiate the observations (using depth, temperature, and salinity as the independent variables – abbreviated to “RFR(DEPTH+TEMP+SAL)” following Table 1). The RFR(DEPTH+TEMP+SAL) model was then used to explore the variation of error in the predictions using the dataset selection error approach described in Sect. 3.2. This builds multiple versions of the same model with different splits of training and test data and yields a distribution of root mean square error in the predicted iodide for withheld data as summarised in the final column of Table 2 and shown graphically in Appendix Fig. A1.
我们采用随机森林回归模型，该模型使用变量构建，直观地假设这些变量具有区分观测结果的合理能力（使用深度、温度和盐度作为自变量 - 缩写为“RFR(DEPTH+TEMP+SAL)”，如下表1 ）。然后使用 RFR(DEPTH+TEMP+SAL) 模型来探索预测中误差的变化，使用第 1 节中描述的数据集选择误差方法。 3.2 .这使用不同的训练和测试数据分割构建了同一模型的多个版本，并产生了保留数据的预测碘化物的均方根误差分布，如表2最后一列中总结并​​在附录图A1中以图形方式显示。

We define outliers here as values greater than the third quartile plus 1.5 times the interquartile range (Frigge et al., 1989). Removing these 49 values categorised as outliers (>309.5 nM) leads to a vast improvement in the RMSE error in the ensemble prediction from 95.1 to 37.6 nM (Table 2). This is shown graphically in Appendix Fig. A1, with the other subsets of the data explored (Table 2). This demonstrates that the high values are not well enough represented by the dataset to be able to be captured by the RFR approach. The removal of these high values from the dataset can also be justified as the driver for these concentrations is not yet well understood (Chance et al., 2014, 2019c; Cutter et al., 2018).
我们在这里将异常值定义为大于第三个四分位数加上 1.5 倍四分位距的值（ Frigge 等， 1989 ） 。删除这 49 个被分类为异常值 ( >309.5 nM) 的结果是，集合预测中的 RMSE 误差从 95.1 nM 大幅改善至 37.6 nM（表2 ）。附录图A1中以图形方式显示了这一点，并探索了其他数据子集（表2 ）。这表明数据集不足以很好地表示高值，无法通过 RFR 方法捕获。从数据集中删除这些高值也是合理的，因为这些浓度的驱动因素尚未得到很好的理解（ Chance 等人， 2014，2019 c ； Cutter 等人， 2018 ） 。

Removing these outliers reduces RMSE in the prediction with the 20 independent model builds from 48.2 to 2.3 nM (third quartile–first quartile). Once these outliers are excluded, more modest changes in average RMSE are then seen if models are built only using coastal or non-coastal data. Figure A1 also shows this is seen when removing lower salinity data (“Salinity ≥30 PSU and no outliers”), which is indicative of estuarine water. This highlights the strength in this approach's ability to predict iodide in different biogeochemical regions (i.e. not just coastal or non-coastal locations).
删除这些异常值可将 20 个独立模型构建的预测中的 RMSE 从 48.2 降低到 2.3 nM（第三个四分位数 - 第一个四分位数）。一旦排除这些异常值，如果仅使用沿海或非沿海数据构建模型，则平均 RMSE 会出现更温和的变化。图A1还显示了在删除较低盐度数据（“盐度≥30 PSU 并且没有异常值”）时看到的情况，这表明是河口水。这凸显了该方法预测不同生物地球化学区域（即不仅仅是沿海或非沿海地区）碘化物的能力。

An additional removal of a single dataset of 19 observations from the Skagerrak strait (Truesdale et al., 2003) was made due to it exerting a disproportionate influence on iodide prediction in high northern latitudes (≥65∘$\ge \mathrm{65}{}^{\circ }$ N), an area that is almost entirely unconstrained by local observations. We note that the Skagerrak is relatively unusual oceanographically, being an estuarine location with high ship traffic, and is considered unlikely to be an analogue for iodine speciation in the Arctic. This is decision is discussed further in the Appendix (Sect. A1), and the predictions made including this dataset are also provided in the shared output (Sect. 5).
额外删除了斯卡格拉克海峡的 19 个观测值的单个数据集（ Truesdale 等， 2003 ），因为它对北高纬度地区的碘化物预测产生了不成比例的影响（ ≥65∘$\ge \mathrm{65}{}^{\circ }$ N），一个几乎完全不受当地观测限制的区域。我们注意到，斯卡格拉克海峡在海洋学上相对不寻常，是一个船舶交通频繁的河口位置，并且被认为不太可能与北极的碘形态类似。这一决定将在附录（ A1节）中进一步讨论，并且包括该数据集在内的预测也在共享输出中提供（第5节）。

From here, only the 1293 observational points excluding outliers and the data from the Skagerrak strait (Truesdale et al., 2003) are used.
从这里开始，仅使用排除异常值的 1293 个观测点和斯卡格拉克海峡的数据（ Truesdale 等， 2003 ） 。

3.4 Selection of ancillary variables and building an ensemble prediction
3.4辅助变量的选择和建立集合预测

To decide which ancillary variables (temperature, salinity, etc.; see Table 1 and Sect. 2) should be used to predict sea-surface iodide concentration, RFR models were built and evaluated with different combinations of variables. Thirty eight combinations were considered (see first column of Appendix Table A2).
为了确定应使用哪些辅助变量（温度、盐度等；参见表1和第2节）来预测海面碘化物浓度，建立了 RFR 模型并使用不同的变量组合进行评估。考虑了 38 种组合（参见附录表A2第一列）。

The top 20 performing models, based on their root mean square error against the withheld data, are plotted in Fig. 2, alongside existing parameterisations. The standard deviation for all predicted values is also shown to illustrate variation in the predictions. A complete list of the performance and of all models built here and their performance is given in the appendix (Table