Ecology

Record-breaking Turkish diver Şahika Ercümen draws attention to plastic pollution in the Bosporus.Credit: Sebnem Coskun/Anadolu Agency/Getty

Next year sees the start of 12 crucial months for the planet — or at least a proportion of it. Important talks on the future of food and agriculture, biodiversity and climate will all happen in 2021, a year later than planned. But there’s one meeting still missing from this list: the United Nations Ocean Conference, originally due to take place in Lisbon in 2020, has not yet been rescheduled for 2021.
For too long, the ocean and seas, 71% of Earth’s surface, have been under-represented at some of the world’s most influential global environmental-policy processes. That is now changing, helped by a powerful initiative led by 14 world leaders — which this week publishes important findings in Nature. These reports come as the UN, together with many others, is preparing to advocate stronger action. (Researchers, non-governmental organizations and the UN refer to ‘the ocean’ rather than ‘oceans’ to emphasize the connectedness of this global ecosystem.)
Part of the reason ocean policy is neglected is the lack of a high-level intergovernmental process through which binding decisions can be made. The marine environment is discussed when world leaders get together for meetings of the UN conventions on biodiversity and climate — but is rarely, if ever, a priority.

This state of affairs prompted the prime ministers of Norway and Palau — both nations with economies dependent on a healthy ocean — to convene some of their peers, including the leaders of Canada, Indonesia and Kenya. Between them, they agreed to do more to protect and improve ocean health, and to safeguard the benefits that humans reap from the marine environment.
The High Level Panel for a Sustainable Ocean Economy was established in 2018, but its members needed scientific advice. They turned to researchers across ocean sciences and asked them to review the literature on the state of the seas and the benefits they provide, before deciding what further action to take.
This week sees a collection of the researchers’ outputs published in the Nature family of journals (see go.nature.com/3kyd0dx). The reports describe the parlous state of ocean health, but they also provide hope. If the ocean is managed more sustainably, species and ecosystems could revive, and could become better sources of sustainable food, energy, materials, livelihoods and, ultimately, planetary well-being.

As the panel’s research advisers write in a Comment article, climate change is warming and acidifying the ocean and depleting ocean oxygen. At the same time, overfishing is removing important species from the food chain, accelerating biodiversity loss. Unsustainable industrial development along coastlines — new and larger ports, hotels and housing developments — are also adding to ocean pollution. “All of these threats erode the capacity of the ocean to provide nutritious food, jobs, medicines and pharmaceuticals as well as regulate the climate. Women, poor people, Indigenous communities and young people are most affected,” the authors say.
Yet the ocean also has potential to help mitigate climate change. If managed more sustainably, the researchers forecast — in preliminary estimates — it could contribute between 6% and 21% of the emissions reductions needed by 2050 to achieve the goal of the 2015 Paris climate agreement, limiting global warming to 1.5 °C above pre-industrial levels.
The ocean also has the potential to contribute many times more renewable energy than it did in 2018, through increasing offshore wind and wave energy. And it could help to produce more food through cultivation of organisms that are not yet widely consumed, such as molluscs and seaweed.
The political leaders in the high-level panel have said that, by 2025, they will sustainably manage 100% of their ocean areas — not just their national waters, but their entire exclusive economic zones, stretching out 370 kilometres from their coasts. These commitments are commendably direct and rooted in science — and so should be welcomed. But they need to be accompanied by a process to ensure that they can be kept.
Held to account
Pledges made by heads of state are too rarely accompanied by monitoring or accountability mechanisms. Yet it is such things — enshrined in international conventions and law — that ensure world leaders are compelled to report periodically on their progress, or lack of it, in protecting biodiversity, the climate and other areas affected by environmental degradation.

Monitoring and accountability, in turn, need indicators of success or failure. Researchers and national statistics offices are in the process of updating the international standard System of Environmental-Economic Accounting — Experimental Ecosystem Accounting (SEEA EEA), which is due to be adopted by the UN Statistical Commission in March. One of the studies in the collection proposes a framework through which existing global ocean data can be used to measure the condition of ocean ecosystems (E. P. Fenichel et al. Nature Sustain. 3, 889–895; 2020). Indicators on which there is a degree of consensus include those for biodiversity, ecosystem fitness and the ability of the ocean to retain greenhouse gases.
Momentum is building for stronger action. The UN is preparing to publish its second World Ocean Assessment sometime in 2021. Next year will also be the start of the UN’s decade devoted to ocean science and sustainable development. And the UN Convention on Biological Diversity is preparing to update its targets to slow down biodiversity loss — including an updated goal for coastal and marine areas under protection.
It is rare for world leaders to take a lead as the high-level panel has done, and they must be commended for their pledge to manage the ocean sustainably. But governments change. The panel’s members know that, one day, they will need to pass on their responsibilities. In some cases, their successors will want to continue their policies, but in others, they won’t — as we know all too well.
That is why we need a mechanism to monitor pledges according to agreed data, tested by a consensus of the research community. Researchers stand ready to play their part. But to help ensure that these vital pledges are kept, sustainable management of the ocean needs a sustainable system of governance, too. More

Atmospheric cabinet concentrations of elements emitted as ultrafine PM during additive laser processing are given in Table 3.
Table 3 Atmospheric concentrations of elements (mg/m3) measured during laser additive processing (n = 2).
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Primary particle formation and size-distribution
For all three instruments studied, the collected PM consisted of complex aggregates/agglomerates with fractal-like geometry (Fig. 1). No more than ten coarser particles with geometric projected diameters between 0.7 and 2 µm were observed on each filter. The elemental compositions were similar to the bulk material and no crystalline phases were identified. The presence of these may be due to sputtering from the melted alloy. No larger particles were seen. An equivalent projected area diameter of primary particles measured by TEM are shown in Fig. 2 and primary particle size-distribution summary statistics is presented in Table 4. The overwhelming number of particles formed in the three processes had equivalent projected area diameters within the 4–16 nm size range, with median sizes of 8.0, 9.4 and 11.2 nm for EOS M 270 dual mode, InssTek MX-Mini and LC-10 IPG-Photonics, respectively. The largest primary particles identified in the size-measurements had diameters of 50.4, 82.0 and 77.5 nm, correspondingly. Compared to previous research of laser ablation of metals where a maximum of the particle size distribution at 6–11 nm, dependent on laser intensity, were observed, the sizes of the primary particles in the laser additive processes studied in this work are similar32. It has previously been shown that the PM generated during manual metal arc, metal inert gas (MIG) and tungsten inert gas welding operations consists of agglomerates with primary particle diameters in the range of 5–40 nm with very few above 50 nm33.
Figure 2

Size distribution (equivalent projected area diameter) of primary particles. Calculated by Minitab 16 software (Minitab Statistical Software, Minitab 16; https://www.minitab.com).

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Table 4 Summary statistics of primary particle sizes in nm.
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Numerical modelling of gas-phase processes
To understand particle growth and oxidation it is essential to locate their trajectories in the zones of heated laser spots. Although it is difficult to visualize tracks of nano-sized particles directly because of their size, as well as gas flow dynamics in vicinity of processed zone, it is, however, possible to perform a close-to-real-life numerical simulation of these gas-phase processes during laser surface treatment of the substrate. In Fig. 3 the presence of toroidal eddies surrounding a hot vertical jet of metal vapour is demonstrated. These vortices remain unchanged in vicinity of a laser spot during all the process of sintering and form a recirculation zone around the heat-affected region. A close look with streamlines plotted from a base of this hot up-stream (Fig. 3b) shows the recirculation zone more clearly. Nano-sized particles due to their extremely low mass (about 5 × 10–16 ng) will exactly follow gas streamlines, finally trapping into that toroidal eddies. However, the particles do not stay in the recirculation zone permanently: they grow and drift to peripheral regions of the vortex, and finally leave it. According to estimations based on our numerical simulation, particle mean residence time in a vortex is about 0.5 ms for a particle of initial diameter of 10 nm and density of 7850 kg/m3.
Figure 3

Simulated temperature and velocity fields during laser processing using EOS M270 dual mode. (a) Dynamics of process. Top: temperature, bottom: velocity magnitude and normalized vectors. Color mapping is the same as is shown in part (b) of this figure. Laser moves from left to the right side. (b) Temperature, velocity and streamlines (in black) close to keyhole. Computations and post-processing have been performed in Ansys Academic Research Fluent, Release 19.2 https://www.ansys.com/products/fluids/ansys-fluent.

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Similar behavior of particles is expected for the DED machine. To verify that, gas flow and temperature dynamics for the InssTek MX Mini machine have also been simulated. Laser power of 200 W is focused in a Gaussian beam having a spot diameter of 1 mm, whereas surface absorbance and penetration depth are the same as in the modeling of the PBF-LB/M machine. Although complete information on inner design of a nozzle mounted in that machine is not available, we primarily oriented on its general view and typical conventional flow rates used in three-stream coaxial nozzles. Computational domain is initially filled with air, and all in-nozzle inlets consist of 99.9% pure argon. We consider even this “approximate” case is still usable to estimate flow pattern near the laser spot. Although the cladding head moves horizontally with speed of 1 cm/s, the flow field is relatively steady. Vaporization-induced puff above the treated surface of steel has a height of about 1 mm. Again, streamlines sampled close to the heat-affected zone represent the gas recirculation regions which are shown in black color on top of the vector velocity field, demonstrating the occurrence of a toroidal vortex caused by the hot vertical gas stream (Fig. 4). In contrary to the PBF-LB/M process, this gas jet cross-collides with a flow moving in opposite direction produced by the cooling gas. Nano-particles (NP) of partially condensed metal vapor should thus be trapped and turned back to the laser-affected zone again, but some of them will follow peripheral streamlines and slide along the treated surface. Estimated particle in-eddy residence time approximately equals 1.5 ms which is about 3 times more than in the PBF-LB/M process.
Figure 4

Simulation of InssTek MX Mini: temperature, velocity and mass fraction of argon. Velocity vector field and streamlines are zoomed in vicinity of a heat-affected zone. Computations and post-processing have been performed in Ansys Academic Research Fluent, Release 19.2 https://www.ansys.com/products/fluids/ansys-fluent.

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The boundary zone of the vortex is located close to the mixing zone of the surrounding air (see Ar mass fraction in its mixture with air in the right part of Fig. 4, where “Ar-air” interface is marked in green color) with a likely forced oxidation of airborne particles because of their possible interaction with oxygen (O) from air.
Various fabrication methods of NP based on vapor deposition have been developed. Laser ablation is a method where very high energy is focused to a solid material for evaporation of light-absorbing materials where the vapor phase is thermodynamically unstable. Under chemical supersaturation vapor-phase atoms/molecules will rapidly and uncontrolled be condensed with a coagulation rate proportional to the square of their number concentration. At high temperatures particles coalesce faster than they coagulate; at lower temperatures loose agglomerates with rather open structures are formed35. In high temperature aerosol reactors NP ( More

Study area
The Beijing–Tianjin–Hebei (BTH) region of China is one of the most economical and active areas in China, containing Beijing, Tianjin, and 11 cities of Hebei Province. According to CSY (2018), the regional GDP of BTH in 2017 contributed 9.77% to the total GDP of China, and its population accounted for 8.09%. However, serious air pollution occurred, and its damage to public health cannot be ignored. According to the Ministry of Environmental Protection (MEP) (2018), among the top 20 most polluted cities, 9 cities belonged to Hebei Province, and Tianjin and Beijing ranked 15th and 19th, respectively. Thus, this study adopted the BTH region as the study area for constructing the PM2.5 concentration forecasting model. Figure 1 shows the Locations of air quality stations in the BTH region.
Figure 1

Locations of air quality stations in BTH region. The color represents the rank of the average daily PM2.5 concentration during 01 Jan., 2015 to 31 Dec., 2017 as described in the bottom of the Figure. (This Figure is drawn by using Matlab software).

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Data
The research data and their description used in this study are listed in Table 1. We collected data from the period of 01 Jan. 2015 to 31 Dec. 2017. The variables included the PM2.5 concentration, meteorological data, the latitude and longitude of the monitoring station, and time stamp data, i.e., the month and week of the observation.
Table 1 List of the research data.
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1.
PM2.5 concentration data: There are 110 air pollution monitoring stations distributed in the BTH region, as shown in Fig. 1. The hourly concentration of PM2.5, PM10, CO, NO2, O3, and SO2 are recorded and published by the Beijing Municipal Environmental Monitoring Center and http://pm25.in/. Station parameters are also recorded, including the latitude and longitude of the station, the month and the week of the observation. Here, we used the mean of the PM2.5 concentration from 0:00 to 23:00 to represent the daily PM2.5 concentration, and the rank of the average daily PM2.5 concentration from 2015 to 2017 is indicated by the color in Fig. 1. It can be found that air pollution is more serious in the south area.

2.
Meteorological data: The meteorological variables considered in this study included temperature, wind speed, wind direction, mean sea level pressure, dew point temperature and total column water vapor. Meteorological data were obtained from CAMS Near-real-time dataset of ECMWF with around 10 km spatial resolution. Particularly, this dataset only provides (U) and V component of wind (i.e., zonal and meridional wind speed), thus, the wind speed and wind direction were obtained by the Eqs. (1) and (2).

$$wind ; speed=sqrt{{u}^{2}+{v}^{2}}$$
(1)

$$wind ; direction=frac{pi }{2}-{mathit{tan}}^{-1}frac{v}{u}$$
(2)

where (u) and v refer to (U) and (V) components of wind, respectively. In addition, to further improve the spatial resolution of temperature, the 1 km spatial resolution Modis temperature product (MOD11A1) were also collected.
Data pre-processing
Due to critical failure or temporary power cutoff, missing values for a long or short periods happened in air pollution monitoring stations24. Similarly, some missing values occur in the ECMWF dataset. We got rid of data of 20 stations which have over 10% missing values in PM2.5 concentration data or ECMWF data. The missing PM2.5 concentration values of remaining stations were interpolated by inverse distance weight method.
Next, time stamp data, including month and day, were one-hot encoded; PM2.5 concentration and meteorological data were centralized and standardized in accordance with Eq. (3):

$${x}_{i}^{*}=frac{{x}_{i}-stackrel{-}{x}}{sigma }$$
(3)

where ({x}_{i}) and ({x}_{i}^{*}) represent the original and transformed observation of a factor (x), respectively; (stackrel{-}{x}) and (upsigma) are the mean and standard deviation of all observations, respectively.
Finally, the temperature data collected from MOD11A1 and ECMWF dataset were merged together to enhance its reliability. Since the spatial resolution of MOD11A1 data is higher, we used MOD11A1 data as basis, and filled its missing values by ECMWF data. Linear regression model was built between the centralized and standardized ECMWF temperature data ((cs_E)) and MOD11A1 data ((cs_M)) as the Eq. (4) shows,

$$c{s}_{M}=0.953842*c{s}_{E}-0.074635$$
(4)

The ({R}^{2}) value of this model was 0.91, indicating a great consistency between them. Therefore, we filled the missing values of (cs_M) by the regression results of corresponding (cs_E) values.
Methods
Figure 2 shows the overall framework of the proposed WLSTME model. As shown in Fig. 2, the model is a hybrid model that integrates three neural networks, including:
(1)
An MLP network to generate the weighted PM2.5 by combing wind speed and direction, geographical distance with historical PM2.5 concentration.

(2)
An LSTM network to address spatiotemporal dependency simultaneously and extract spatiotemporal features.

(3)
Another MLP network to optimize the prediction by integrating the spatiotemporal features and weather forecast data.

Figure 2

(a) Overall framework of WLSTME. The red, blue and green flags stand for the central site, K nearest sites, and other sites, respectively. r represents the time lag; (b) Structure of MLP layer; (c) Structure of the memory cell of LSTM layer. xt and ht are the inputs.

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In detail, the three network works together to form an organic whole to achieve the daily PM2.5 prediction. Firstly, the MLP was used to combine historical wind speed and wind direction, the geographical distance between central sites and neighbor sites with corresponding days’ PM2.5 data of neighbor sites, and generate the weighted PM2.5. Then, the generated weighted PM2.5 of the neighbor sites in the past ten days were merged with the historical PM2.5 data of the central station, and input into the LSTM network to address the spatial and temporal dependence simultaneously and extract spatiotemporal features. Finally, another MLP was used to conduct bias adjustment by integrating the spatiotemporal features produced by LSTM with the central site’s meteorological data and time stamp data.
The input of WLSTME model consists of two parts (blue arrows in Fig. 2): (1) historical air quality (PM2.5), latitude and longitude; historical meteorological data (weather, temperature, pressure, humidity, wind speed, wind direction) of the target site and nearby sites. ; (2) Weather forecast data (weather, wind direction, wind level, up and down temperature) of the target site. The output of WLSTME model is the PM2.5 forecast value of the target site the next day.
MLP for generating the weighted PM2.5
MLP can theoretically approximate any Borel measurable function with arbitrary precision25. We constructed a three-layer MLP spatial correlation processor to generate weighted PM2.5 series data for each neighbor site. Neighbor sites were defined as the K nearest surrounding sites to the central site. Since pollutants are transported among areas based on wind, air pollution of the central sites are spatially correlated with that of neighbor sites. However, the distribution of monitoring stations is not even. Consequently, the distance between neighbor sites and the central site is different for different central sites. For example, the density of stations in the south area is much sparser than Beijing, as Fig. 1 shows. Thus, for central sites in the south area, the selected neighbor sites were more distant, and the spatial correlation was lower than that for sites in Beijing. Based on the above consideration, the geographical distance of the selected neighbor sites should be considered in the model.
The three-layer MLP integrates the distance and wind of neighbor sites with its PM2.5 to generate weighted PM2.5 data for each neighbor site j of central site i. Figure 3 shows the structure of MLP. Given ({PM2.5}_{ jt}) and ({v}_{jt}) represent the PM2.5 concentration and wind speed of the (jth) neighbor at time t, respectively; ({d}_{ij}) represents the distance between the central site (i) and its (mathrm{jth}) neighbor site; ({uptheta }_{ijt}) represents the angle between the wind direction of (mathrm{jth}) neighbor site at time (t) and the edge between (i) and (j). ({H}_{1},dots ,{H}_{n}) are neurons of the hidden layer, and ({WPM2.5}_{jt}) is the weighted PM2.5 concentration, which is calculated by the Eqs. (5) and (6).
Figure 3

The structure of the three-layers MLP model.

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$${H}_{s}={g(omega }_{1s}^{1}{PM2.5}_{jt}+{omega }_{2s}^{1}{d}_{ij}+{omega }_{3s}^{1}{v}_{jt}+{omega }_{4s}^{1}{theta }_{ijt}$$
(5)

$${WPM2.5}_{ jt}={sum }_{s=1}^{n}{omega }_{s}^{2}{H}_{s}$$
(6)

where (g) is the activation function used for the nonlinear transformation of inputs. (omega) is the weight between the neuron of previous layer and the next layer.
LSTM for extracting spatial–temporal feature
LSTM is a special recurrent neural network, with its recurrent neuron simultaneously captures long and short dependencies in time series data. LSTM has been used in many fields, such as financial market predictions26, epileptic seizures27, and reservoir operation28. All of the LSTM models used in these fields exhibited better performance than many other machine learning methods. The LSTM model used in our model was a two-layer stateful LSTM, which used the state of the current batch of LSTM samples as the initial state of the next batch of samples. It is more suitable for processing long-term time series data than the other models. The structure of the recurrent memory cell of the LSTM model is shown in Fig. 4.
Figure 4

The illustration of two-layers LSTM model. ({x}_{t}) and ({h}_{t}) are the inputs and outputs at time t respectively.

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The bottom layer of the proposed LSTM FRAME corresponds to the input layer. The middle core layer comprises two LSTM layers, and the output layer follows. Each neuron of the LSTM layer has an architecture similar to that in the right part of Fig. 4. Three key gates, namely, forget gate (({f}_{t})), input gate (({i}_{t})), and output gate (({o}_{t})), of LSTM are designed to control the memory of new information and to forget old information. The values of the three gates are updated with time respectively by Eqs. (7), (8), and (9).

$$f_{t} = sigma left( {W_{f} cdot left[ {h_{t – 1} ,x_{t} } right] + b_{f} } right),;;i_{t} = sigma left( {W_{i} cdot left[ {h_{t – 1} ,x_{t} } right] + b_{i} } right),$$
(7)

$$widetilde{{C_{t} }} = tanhleft( {W_{C} cdot left[ {h_{t – 1} ,x_{t} } right] + b_{C} } right),;;C_{t} = f_{t} cdot C_{t – 1} + i_{t} cdot widetilde{{C_{t} }}$$
(8)

$$o_{t} = { }sigma left( {W_{o} cdot left[ {h_{t – 1} ,x_{t} } right] + b_{o} } right),;;h_{t} = o_{t} cdot tanhleft( {C_{t} } right)$$
(9)

where ({x}_{t}) and ({h}_{t}) are the inputs and outputs of time (t), respectively; (sigma) and hyperbolic tangent are widely used activation functions; (W) and (b) are the weight matrix and bias vector, respectively.
In detail, LSTM is designed to extract spatiotemporal features from the pollution data of central site and neighbor sites to make a prediction. The weighted PM2.5 series data of neighbor sites and PM2.5 concentration observation data of the central site were merged as a 2D matrix, with each column represented the historical PM2.5 concentration of the central site or weighted PM2.5 concentration of a neighbor site. The size was (mathrm{r}times (mathrm{K}+1)), where r was time lag, and K was the number of selected neighbor sites. We placed this matrix into a two-layer LSTM model so that their spatial and temporal dependence and synthetic action could be considered simultaneously. The output of the LSTM model is called pre-prediction.
MLP weather forecasts optimizer
Finally, auxiliary variables were introduced to the WLSTME model to promote prediction accuracy. The auxiliary variables considered in this study included meteorological data (temperature, wind speed, dew point temperature, mean sea level pressure and total column water vapor), time stamp data (day of week and month of the year), and latitude of the central site at time T. We integrated the auxiliary variables with the spatiotemporal features extracted by LSTM and input them into MLP to output the prediction of the next day’s PM2.5 concentration of the central site. The structure of MLP was the same as Fig. 3, however, the input and output were substituted by the spatiotemporal features and PM2.5 concentration prediction, respectively.
Evaluation methods
We predict real-values of PM2.5 concentration for the next day. Three criteria, namely, mean absolute error (MAE), root mean square error (RMSE), and total accuracy index (p), were used in the experiments to evaluate the effectiveness of our model. Their definitions are given in Eqs. (10), (11) and (12):

$$MAE=frac{1}{n}sum_{begin{array}{c}\ \ i=1end{array}}^{n}left|{y}_{i}-{y}_{i}^{*}right|$$
(10)

$$RMSE=sqrt{frac{1}{n}sum_{i=1}^{n}{({y}_{i}-{y}_{i}^{*})}^{2}}$$
(11)

$$p=1-frac{sum_{i=1}^{n}left|{y}_{i}-{y}_{i}^{*}right|}{sum_{i=1}^{n}{y}_{i}}$$
(12)

where (n) is the number of samples, ({y}_{i}) is the observation of the (mathrm{i})th sample, and ({y}_{i}^{*}) is the (mathrm{i})th forecasting value. In addition, we employed the spatial anomaly correlation (ACC) and the temporal correlation coefficient (TCC) as the evaluation metrics, which are defined as in the following equations:

$$stackrel{-}{{y}_{i}}=frac{1}{N}{sum }_{j=1}^{N}{y}_{ij}, quad stackrel{-}{{y}_{i}^{*}}=frac{1}{N}{sum }_{j=1}^{N}{y}_{ij}^{*}$$
(13)

$${Delta y}_{ij}={y}_{ij}-stackrel{-}{{y}_{i}}, quad {Delta y}_{ij}^{*}={y}_{ij}^{*}-stackrel{-}{{y}_{i}^{*}}$$
(14)

$$ACC=frac{1}{N}{sum }_{j=1}^{N}frac{{sum }_{i=1}^{M}({Delta y}_{ij}-stackrel{-}{{Delta y}_{j}})({Delta y}_{ij}^{*}-stackrel{-}{{Delta y}_{j}^{*}})}{sqrt{{sum }_{i=1}^{M}{({Delta y}_{ij}-stackrel{-}{{Delta y}_{j}})}^{2}{sum }_{i=1}^{M}{({Delta y}_{ij}^{*}-stackrel{-}{{Delta y}_{j}^{*}})}^{2}}}$$
(15)

$$TCC=frac{1}{M}{sum }_{i=1}^{M}frac{{sum }_{j=1}^{N}({y}_{ij}-stackrel{-}{{y}_{i}})({y}_{ij}^{*}-stackrel{-}{{y}_{i}^{*}})}{sqrt{{sum }_{j=1}^{N}{({y}_{ij}-stackrel{-}{{y}_{i}})}^{2}{sum }_{j=1}^{N}{({y}_{ij}^{*}-stackrel{-}{{y}_{i}^{*}})}^{2}}}$$
(16)

where ({y}_{ij}) and ({y}_{ij}^{*}) represent the observed and predicted value of station (i) in day (j), respectively. (M) and (N) represent the count of stations and days of the test, respectively. More

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