Observation-Guided Meteorological Field Downscaling at Station Scale: A Benchmark and a New Method

JOURNAL OF L A T E X CLASS FILES, VOL. 14, NO. 8, A UGUST 2021 1 Observ ation-Guided Meteorological Field Do wnscaling at Station Scale: A Benchmark and a Ne w Method Zili Liu, Hao Chen † Member , IEEE , Lei Bai, W enyuan Li, K eyan Chen, Zhengyi W ang, W anli Ouyang, Zhengxia Zou and Zhenwei Shi † Senior Member , IEEE Abstract —Downscaling (DS) of meteorological variables in- volves obtaining high-resolution states from low-resolution mete- orological ﬁelds and is an important task in weather for ecasting. Pre vious methods based on deep learning treat downscaling as a super -resolution task in computer vision and utilize high- resolution gridded meteorological ﬁelds as supervision to improv e resolution at speciﬁc grid scales. However , this approach has struggled to align with the continuous distrib ution characteristics of meteorological ﬁelds, leading to an inherent systematic bias between the downscaled results and the actual observations at meteorological stations. In this paper , we extend meteorological downscaling to arbitrary scattered station scales, establish a brand new benchmark and dataset, and retrieve meteorological states at any given station location from a coarse-resolution meteorological ﬁeld. Inspired by data assimilation techniques, we integrate observational data into the do wnscaling process, pr ovid- ing multi-scale observ ational priors. Building on this foundation, we propose a new downscaling model based on hypernetwork architectur e, namely HyperDS , which efﬁciently integrates differ - ent observational information into the model training, achieving continuous scale modeling of the meteorological ﬁeld. Through extensive experiments, our proposed method outperf orms other specially designed baseline models on multiple surface variables. Notably , the mean squar ed err or (MSE) f or wind speed and surface pressure impro ved by 67% and 19.5% compared to other methods. W e will release the dataset and code subsequently . Index T erms —Meteorological ﬁeld downscaling, remote sens- ing, hyper networks, earth observation. I . I N T RO D U C T I O N The work was supported by the National Natural Science Foundation of China under Grants 62125102, the National Ke y Research and Dev elopment Program of China (Grant No. 2022ZD0160401), the Beijing Natural Science Foundation under Grant JL23005, and the Fundamental Research Funds for the Central Univ ersities, the National Ke y Research and De velopment Program of China(Grant No.2022ZD0160101). (Corresponding author: Zhenwei Shi (e- mail:shizhenwei@buaa.edu.cn)) Zili Liu, K eyan Chen and Zhenwei Shi are with the Image Processing Center , School of Astronautics, with the Beijing Ke y Laboratory of Digital Media, and with the State Ke y Laboratory of V irtual Reality T echnology and Systems, Beihang Univ ersity , Beijing 100191, China, and also with the Shanghai Artiﬁcial Intelligence Laboratory , Shanghai 200232, China. Hao Chen, Lei Bai, and W anli Ouyang are with Shanghai Artiﬁcial Intelligence Laboratory , Shanghai 200232, China. W enyuan Li is with the Department of Geography , Univ ersity of Hong K ong, Hong K ong, China. Zhengyi W ang is with the School of Oceanography , Shanghai Jiao T ong Univ ersity , Shanghai 200030, China, and also with Shanghai Artiﬁcial Intel- ligence Laboratory , Shanghai 200232, China. Zhengxia Zou is with the Department of Guidance, Navigation and Control, School of Astronautics, Beihang Uni versity , Beijing 100191, China, and also with Shanghai Artiﬁcial Intelligence Laboratory , Shanghai 200232, China. I N recent years, the application of artiﬁcial intelligence technologies such as deep learning in weather forecasting has garnered signiﬁcant attention [1]–[3]. These efforts uti- lize large-scale gridded historical meteorological ﬁeld data, combined with adv anced models from computer vision, and hav e demonstrated powerful performance in many forecasting tasks [4]–[7], e ven surpassing the long-developed numerical weather prediction systems [8]. Nevertheless, the reliance on methodologies from the ﬁeld of computer vision has led to the acquisition of image-like meteorological ﬁeld data in the form of ﬁxed and relativ ely coarse resolution. This approach is at odds with the intrinsically multi-scale nature of meteorological variables. Consequently , to obtain meteorological variables at varying scales and resolutions, downscaling has become an indispensable post-processing task within operational forecast- ing [3], [9]. The objectiv e of downscali ng in weather forecasting is typically to map coarse-resolution global-scale meteorological ﬁelds to high-resolution regional-scale ﬁelds [10]. This setup appears to be highly analogous to the task of image super- resolution in computer vision [11]. The traditional dynamic downscaling methods [12] are akin to numerical weather prediction techniques, in volving the numerical solution of atmospheric dif ferential equations at a regional scale. This process is highly computationally demanding, particularly when the grid resolution is very high. As a result, machine learning-based downscaling methods, primarily those in volv- ing deep learning, hav e recently received increased attention as a parallel approach [3], [9], [10], [13], [14], [14]–[29]. Most pre vious deep learning-based downscaling works directly employ models and methods from image super-resolution tasks due to the similarity between the two tasks. Meteorological ﬁeld data is treated as an image to achiev e super-resolution at a ﬁxed resolution and ﬁxed upscaling factor , which is direct and efﬁcient. Howe ver , this direct application of existing methods also means that the models lack specialized design and ﬂex- ibility tailored to the unique characteristics of meteorological data. Unlike natural images that are directly captured through camera sensors, gridded meteorological ﬁeld data are obtained by fusing and assimilating multi-source, multi-scale, and multi-modal observational and forecast data, typically referred to as analysis data or r eanalysis data. The observational infor- mation employed generally includes satellite remote sensing images, ground observation stations, radiosondes, and so on. JOURNAL OF L A T E X CLASS FILES, VOL. 14, NO. 8, A UGUST 2021 2 A speciﬁc meteorological v ariable at a particular pixel can be considered as the average of all observed and predicted values within that pixel area. For instance, the widely used ERA-5 reanalysis data [30] hav e a temporal resolution of 1 hour and a spatial resolution of 0 . 25 ◦ . The state v alue of any giv en pixel can be regarded as the av erage of all observations and forecast results within the 0 . 25 ◦ × 0 . 25 ◦ grid ov er 1 hour . The same applies to forecast ﬁelds derived from analysis and reanalysis data. As a result, for meteorological ﬁelds with ﬁxed resolution, although each grid can be considered as the av erage of all observations, many sub-grid observ ations cannot be effecti vely represented. Howe ver , in practical applications, we aim to obtain the meteorological state at a speciﬁc precise location through the giv en gridded meteorological ﬁeld, rather than merely obtaining the high-resolution gridded meteorological ﬁelds. The absence of sub-grid information results in a signiﬁcant deviation between the state values of the meteorological ﬁeld and the scattered stations [31]. Therefore, for the downscaling of meteorological variables, it is crucial to determine how to increase resolution while accurately recov ering information at the sub-grid scale. A straightforw ard method of reco vering sub-grid information is to use high-resolution real-time obser- vational data with multi-scale resolution to guide the down- scaling task. Most of the e xisting do wnscaling frameworks based on deep learning are inspired by super-resolution tasks. They achie ve downscaling solely by learning the mapping from low-resolution to high-resolution images, which does not allow for the integration of multi-scale observations into the model’ s training and inference processes. W ith its ﬁxed super-resolution factor , the resulting downscaled output is also gridded and does not provide a continuous representation of the meteorological ﬁeld. This makes it challenging to general- ize well to scattered stations. Additionally , to the best of our knowledge, there currently exists no uniﬁed benchmark and dataset for the downscaling of meteorological ﬁelds av ailable to researchers in the ﬁeld. Thus, establishing a reasonable downscaling task speciﬁcally tailored to the meteorological ﬁeld is of critical importance. T o address the aforementioned issues, our paper ﬁrst con- structs a benchmark for do wnscaling meteorological ﬁelds, guided by multi-source, multi-scale, and multi-modal ob- servational data. Our goal is to downscale lo w-resolution meteorological ﬁelds to the scale of arbitrary scatter points. Speciﬁcally , the paper selects ERA5 reanalysis data [30] as the meteorological ﬁeld data to be do wnscaled. For observa- tional data, we utilize remote sensing images from the ne w generation geostationary meteorological satellite Himaw ari-8 (H8) [32] at L1-lev el as high-resolution gridded-scale indirect observational data. Additionally , we employ meteorological observation station data obtained from the W eather2K dataset [33] as direct observational data at the scatter station scale. This task setting is crucial for the do wnscaling of meteorolog- ical v ariables because it allo ws for the utilization of multi-scale observational information, and it can yield downscaling results that are adaptable to multiple scales. The difference between the previous downscaling task and the proposed benchmark is illustrated in Fig. 1. (a) Previous super-r esolution-based downsc aling with fixed scale (b) Our proposed ob servation-guided down scaling with station sca le Low Resolution Field L o w R e s o l u t i o n F i e l d Encoder Decoder Downscale Model Encoder Decoder Downscale Model 4x Downscale Output RS Imag e Scat t er St ati on s Ob ser v ati o ns Low Resolution Field Sati o n-Sc ale Ou tp ut Fig. 1. The difference between the previous SR (super-resolution)-based downscaling pipeline with ﬁxed grid-lev el scale [10] (a), and the proposed observation-guided downscaling pipeline with arbitrary scatter station-level scale. In response to the established benchmark, inspired by the ability of implicit neural representation methods [34] in computer vision to continuously model two-dimensional and three-dimensional data, and combined with a data-conditioned hypernetworks structure [35], we propose a nov el model for the continuous resolution do wnscaling of meteorological ﬁelds, named HyperDS . HyperDS uses H8 observ ations as the model’ s data-conditioned input and takes W eather2K station data as supervision at the scatter station scale. The overall architecture of HyperDS can be divided into a dual-branch hypernetwork and a target network . The former consists of two encoders based on con volutional neural networks that are used to e xtract semantic features from the lo w-resolution mete- orological ﬁeld and H8 data, respectiv ely . Follo wing these, an implicit r etrieval model employs a cross-attention mechanism to implicitly learn the retriev al process from satellite imagery to meteorological ﬁelds, thereby efﬁciently integrating H8 data into the downscaling process. This results in the generation of high-lev el feature vectors that contain fused information. The target network is based on a multilayer perceptron (MLP), whose weights are generated from the fused features out- put by the hypernetwork. It achiev es continuous-resolution downscaling at arbitrary locations by inputting the coordinate values of the target location and obtaining the corresponding meteorological state variables. W e hav e also devised a training technique utilizing sub-grid sampling, and in combination with supervisory data from observational stations, it effecti vely reconstructs accurate state values for meteorological variables at the sub-grid level. W e established sev eral baseline methods and compared them with the proposed method under the condition of identi- cal input and supervision data. HyperDS shows superior do wn- scaling performance at the scatter station scale. Additionally , through more extensi ve analysis and ablation experiments, we JOURNAL OF L A T E X CLASS FILES, VOL. 14, NO. 8, A UGUST 2021 3 also veriﬁed the importance of incorporating observational data for the task of downscaling with multi-scale generaliza- tion. W e hope that more researchers in the ﬁeld will engage in further studies on this new benchmark, aiming to achiev e more ef ﬁcient continuous-resolution modeling of meteorolog- ical ﬁelds and more effecti ve integration of observational data. T o summarize, the main innovati ve contributions of this paper include the following three points: • T aking into account the characteristics of the meteoro- logical variables, we have redesigned a ne w downscaling benchmark that integrates multiple observ ations into the downscaling process, enabling arbitrary scatter stations downscaling and continuous meteorological ﬁeld model- ing. • Based on this new benchmark, we propose a novel model structured around a data-conditioned hypernet- works architecture, namely HyperDS , which achieves scatter station-scale downscaling of meteorological ﬁelds. • Through the design of fair baseline models and extensi ve experiments, we have validated the effecti veness of the proposed new model, which signiﬁcantly outperforms comparativ e methods at the scale of scattered stations. I I . R E L AT E D W O R K In this section, we will brieﬂy introduce and re view the work related to the proposed benchmark and model in this paper . A. Meteor ological F ield Downscaling The objectiv e of downscaling meteorological ﬁelds is to ob- tain accurate weather forecast results with ﬁne granularity and high resolution as required [3], [10]. T ypically , meteorologi- cal forecast data generated by operational global forecasting systems are produced on a relatively coarse-resolution grid. Currently , the highest resolution global forecast and reanalysis data are provided by the European Centre for Medium-Range W eather Forecasts (ECMWF), with their operational Inte grated Forecasting System (IFS) and ERA-5 analysis [30] with a spatial resolution of 0 . 25 ◦ and temporal resolution of 1 hour . T o obtain higher-resolution regional-scale weather states, there hav e been numerous downscaling efforts in the past. Here, we focus our research on methods based on deep learning. Due to the similarity between the task of downscaling and the task of super-resolution in the ﬁeld of computer vision, the vast majority of previous work has been in- spired by related efforts in the ﬁeld of super-resolution. One of the most mainstream approaches is the use of super- resolution networks, such as UNet [36], with an encoder- decoder structure based on CNN [13], [16]–[24] and Trans- former [25]. Furthermore, due to the successful application of generativ e modeling techniques in the ﬁeld of super- resolution, many pre vious studies have also applied Generativ e Adversarial Networks (GANs) and Diffusion models to the task of do wnscaling meteorological ﬁelds, to obtain results with richer texture information [14], [26]–[28]. These studies solely utilize high-resolution meteorological ﬁeld data for supervision, learning the mapping process from low-resolution meteorological ﬁelds to high-resolution ones [9]. Howe ver , the aforementioned methods are all direct applications of super-resolution models and do not incorporate special designs tailored to the characteristics of meteorological variables. They merely achiev e downscaling results at speciﬁc magniﬁcations following high-resolution supervisory data. Some recent works on simulating ﬂuid ﬁeld data [37] have attempted to achie ve grid-independent continuous-resolution downscaling and have integrated physical information as prior [38]. Howe ver , the relev ant physical information and data are dif ﬁcult to apply in the context of real-world data. Our recent work DeepPhysiNet [39] bridges physical laws and deep learning for continuous weather modeling on real-world weather data. But above methods do not make use of sub-grid observational data as an auxiliary . Moreov er, most studies focus solely on downscaling a single type of meteorological variables, such as temperature or precipitation, and are unable to simultaneously process multiple meteorological variables. Addressing the issues present in previous downscaling ef- forts, we ha ve speciﬁcally designed a continuous downscaling benchmark, combined with multi-scale observational data, tailored to the characteristics of meteorological variables. Our new model ef fectively recovers sub-grid states within coarse- resolution meteorological ﬁelds. Moreo ver , we hav e performed downscaling on ﬁ ve surface v ariables, which helps in obtaining more comprehensi ve meteorological state information at the scale of scatter stations. B. Ima ge Super Resolution The widespread application of deep learning in meteorolog- ical downscaling is inseparable from the rapid dev elopment of image super-resolution tasks in the ﬁeld of computer vision. The following is a brief introduction to the related work in image super-resolution (SR). The ﬁeld of image super-resolution (SR) has witnessed a signiﬁcant transformation with the advent of deep learning techniques [11]. Pioneering work, Super-Resolution Con volu- tional Neural Network (SRCNN) [40], demonstrated the effec- tiv eness of deep learning for this task. Building on this foun- dation, many studies have proposed various super-resolution networks based on CNN-based encoder-decoder structures, enhancing the performance of super-resolution tasks [41]– [43]. W ith the de velopment of foundational models in vision, sev eral super-resolution models based on GANs [44], [45] and T ransformers [46], [47] ha ve also been proposed. Ho wev er , the aforementioned super-resolution models are only capable of achieving super-resolution at ﬁxed magniﬁcations. Inspired by implicit neural representations [34], recent works hav e begun to explore super -resolution tasks with continuous resolutions [48], [49]. The aim is to achiev e super-resolution at any arbitrary position by learning the mapping from coordinates to RGB v alues. Howe ver , super-resolution methods based on implicit neural representations suf fer from a lack of sub-grid supervision, resulting in what is called continuous-resolution being merely a more sophisticated form of smoothing. There is scarcely any existing work that has introduced super-resolution methods based on implicit neural represen- tations into the realm of meteorological do wnscaling. Further- more, unlike image super-resolution, meteorological variables JOURNAL OF L A T E X CLASS FILES, VOL. 14, NO. 8, A UGUST 2021 4 T ABLE I M E TE OR O LO GI CA L V A R IA B L E S U S ED F O R DO W NS CA L I N G . Long Name Short Name Description Unit 10m u-component of wind u 10 Eastward component of the wind speed, at the height of 10 meters abov e the surface of the Earth. m/s 10m v-component of wind v 10 Northward component of the wind speed, at the height of 10 meters abov e the surface of the Earth. m/s 2m temperature t 2 m T emperature of air at 2m above the surface of the land, sea or inland waters. K surface pressure sp Pressure of the atmosphere at the surface of land, sea and inland water . hP a total precipitation in 1 hour tp 1 h Accumulated liquid and frozen water, comprising rain and snow , that falls to the Earth’s surface in 1 hour . mm often include a wealth of sub-grid station observational infor- mation, which can better assist models in learning information at continuous locations. Therefore, we incorporate scatter grid observations as auxiliary information into our benchmark, combined with high-resolution remote sensing observations, in the hope of ef fectively integrating multi-scale observ ational data to recover sub-grid meteorological states and achieve meteorological downscaling at scatter station scale. C. Hypernetworks Hypernetworks [50] are the type of model architecture that utilizes one network (commonly referred to as the hypernet- work) to predict the weights of another network (typically called the target network). Compared to traditional network architectures, hypernetworks offer more ﬂexibility in their structure and input/output modalities. They have been widely applied across v arious ﬁelds such as computer vision, solv- ing differential equations, and uncertainty quantiﬁcation [35]. Lev eraging the hypernetwork structure, the traditional per- sample optimization approach of implicit neural representa- tions can be transformed into a data-conditioned hypernetwork learning architecture. This structure allows for the learning of the target network’ s parameters based on dif ferent input samples, and the design of the target network’ s input and output according to the requirements of the task. Re garding the application of hypernetworks to do wnscaling in meteorological ﬁelds, to the best of our knowledge, there are currently no similar ef forts. Giv en the characteristics of hypernetwork structures, they are particularly suitable for meteorological data, which often comprises multi-modal data types. There- fore, the HyperDS we propose utilizes the hypernetw ork model structure and has been speciﬁcally designed to cater to the characteristics of the downscaling task. I I I . P RO B L E M S E T T I N G In this section, we will introduce the observation data- guided downscaling benchmark speciﬁcally designed based on our understanding of meteorological downscaling tasks. This includes a description of the benchmark, the datasets we used, and the ev aluation metrics. A. Observation-Guided W eather Downscaling at Station-Scale 1) T ask Description: Unlike the objectives of previous downscaling or super-resolution tasks, which were to obtain high-resolution grid data, it is very important to capture the meteorological state at any gi ven scatter station location, and this has signiﬁcant practical value [31]. Ho wever , the results produced by most current meteorological tasks are structured gridded data, which need to be further processed through methods such as interpolation to obtain the state v alues at the scatter point locations of interest. As a result, simple interpolation without any learnable process creates an inherent bias between the gridded data and the scatter stations. There- fore, it is crucial to design specialized methods to effecti vely downscale gridded meteorological ﬁelds to scatter points and minimize the inherent bias between them. T o address this issue, inspired by data assimilation [51]– [54], we realize that gridded meteorological ﬁeld data are obtained through the integration of multi-source, multi-scale observational data, and gridded model forecast result. There- fore, using observational data to guide the do wnscaling of meteorological ﬁelds is a very direct and reasonable ap- proach. This allows us to recov er sub-grid information of low-resolution gridded meteorological ﬁelds through multi- scale, multi-resolution observational data, thereby achieving the purpose of downscaling at scatter station scale. Speciﬁcally , we classify the observational data into two categories: one is the gridded high-resolution indirect observa- tional data (such as satellite observ ations), and the other is the scattered sub-grid direct observational data (such as weather observation stations). This also conforms to the observation type settings used in the operational assimilation forecasting in actual meteorological services [52]. Given multiple low spatial resolution meteorological ﬁelds data F input ∈ R 1 × V × LH × LH at a certain time step, gridded high-resolution indirect obser- vational data sequence O ∈ R T × C × T H × T W and scattered sub-grid direct observational data S ∈ R 1 × V × N , where V is the number of meteorological variables, T and C is the number of gridded observ ation frames and channels, N is the number of scatter observations. our goal is to obtain the meteorological state values F output ∈ R 1 × V × M at any M scatter point locations by: F output = Φ( F input | Θ( O ) , S ) (1) where Θ( · ) is a function that maps the indirect observ ational data into the meteorological variable domain. Φ( · ) is a down- scaling model that is used for downscaling to the scatter station scale. It should be noted that, in order to verify the generalization ability of the downscaling process for different scatter point locations, we require that the N points in S and M points in F output are disjoint. Under such a setting, downscaling to multiple grid scales or random scatter point JOURNAL OF L A T E X CLASS FILES, VOL. 14, NO. 8, A UGUST 2021 5 T ABLE II D AT A S ET U S E D I N TH I S B E N C HM AR K , P E R I OD : 2 0 1 7 -0 1 - 0 1 T O 2 0 21 -0 8 - 3 1. Data Name Data T ype Resolution Descriptions ERA-5 Reanalysis [30] Meteorological Field 0 . 25 ◦ , 1 hour Meteorological ﬁelds of 5 surface variables in T ab . I. Himawari-8 L1 Gridded data [32] High-resolution Gridded Observations 5 km , 10 min Rreﬂectance of channel ’albedo 03’, ’albedo 05’, ’tbb 08’ and ’tbb 15’ W eather2K [33] Scatter station Observ ations sub-grid, 1 hour Observation state of air pressure, temperature, wind speed, and total precipitation in 1 hour . Fig. 2. The study area and scatter stations used in our paper . The red dots represent the training stations, the blue dots represent the validation stations and the yellow dots represent the test stations. scales can be achie ved by altering the positions of the target points. 2) Meteor ological V ariables Selection: In order to select signiﬁcant meteorological variables to verify the ef fectiv eness of the downscaling method, we analyzed the characteristics of the observational data and specially selected ﬁve surface variables as the focus of our benchmark: u -component wind ( u 10 ), v -component wind ( v 10 ), 2-meters temperature t 2 m , surface pressure ( sp ) and total precipitation in 1 hour ( tp 1 h ). For details please refer to T ab . I. W e chose these ﬁve variables primarily because the observational data includes the afore- mentioned v ariables, or the values of related variables can be roughly inferred through indirect observations, or there is an implicit correlation between the observational information and the variables. B. Dataset This subsection will introduce the actual data used for the proposed benchmark, with the main data information available in T able II. Based on the observ ational data and meteorological ﬁeld data we used, we selected the research area with a boundary of 80 ◦ E to 136 ◦ E and 18 ◦ N to 54 ◦ N, as sho wn in Fig. 2. This area is an intersection of all the regions covered by all kinds of data we used. 1) Meteor ological F ield Data: W e select the widely recog- nized ERA5 reanalysis data [30] as the meteorological ﬁeld data. Its original resolution is 0 . 25 ◦ , covering the globe, with a temporal resolution of 1 hour . The ERA5 reanalysis data has been widely used in the ﬁeld of meteorological forecasting based on deep learning [55], [56], and it is employed as both the initial ﬁeld and supervision data for models [4]–[7]. For our task, we hav e extracted data for the study area and, through the operation of average pooling, do wnsampled the data to a spatial resolution of 1 ◦ to serve as input for the model. This setup enables us to provide high-resolution grid supervision. It should be noted that previous do wnscaling work was mostly based on forecasting tasks, which primarily in volv ed downscaling coarse-resolution forecast ﬁelds and utilizing high-resolution analysis data for supervision [3], [25]. This setting is typically taken from the perspectiv e of practical operational applications. Different from its starting point, our benchmark aims to study more effecti ve downscaling methods at the scale of scattered stations based on deep learning. Hence, we hope to utilize readily av ailable public data to provide as many complete samples as possible for model training. How- ev er , most model forecast ﬁelds and high-resolution analysis data are often difﬁcult to obtain, or they have a low temporal resolution [57], making it challenging to meet the requirements for a large sample size. Therefore, we hav e chosen the most commonly used ERA5 reanalysis data, which ensures the fulﬁllment of our task requirements. The methods de veloped on it can also be well extended to situations where the forecast ﬁelds are used as inputs. 2) Observation Data: V arious observation data are crucial to forming a structured grid of meteorological ﬁelds. In the ﬁeld of meteorology , data assimilation tasks [51]–[54] speciﬁcally study how to integrate dif ferent observ ation data into forecast ﬁelds, improving the performance of forecast models based on real-time observ ations. Integrating obser- vational data effecti vely into meteorological ﬁelds to obtain more accurate meteorological states at dif ferent locations is an important research direction. W e hope to enhance the accuracy of downscaling by incorporating observational information into downscaling tasks. On the one hand, using observational information to improve the accuracy of do wnscaling, and on the other hand, treating downscaling as a fundamental task to explore effecti ve methods for integrating observational data into meteorological ﬁelds. Based on the task description provided earlier , we selected the L1 gridded data from the next-generation geostationary meteorological satellite Himaw ari-8 [32] as the gridded high- resolution indirect observational data, and we chose the station data set provided by the W eather2K dataset [33] as the scattered sub-grid direct observational data. Belo w is a brief introduction to the two types of observ ational data: JOURNAL OF L A T E X CLASS FILES, VOL. 14, NO. 8, A UGUST 2021 6 Himiwari-8 L1 Gridded Data [32] is generated by J AXA/EORC from the Himawari Standard Data with re- sampling to equal latitude-longitude grids. It includes 16 spectral bands, with a spatial resolution of up to 2 km and a temporal resolution of 10 minutes, obtained from the Advanced Himaw ari Imager (AHI) onboard the Himawari-8 satellite. Due to storage constraints, we primarily downloaded the version with a 5 km spatial resolution and cropped the data to the research area of our interest. Furthermore, to reduce the memory footprint of the input data, we empirically selected four representati ve bands from the visible, near-infrared, and far -infrared spectral ranges. It should be noted that, as we are using Lev el 1 observ ational data rather than the results of the satellite retrie val of meteorological variables, the designed model is required to learn the state values of meteorological variables from the indirect satellite radiance v alues. This also implies that the retrie val process is inherently included in our task. W eather2K dataset [33] was originally designed for mesoscale weather forecasting tasks. It comprises hourly ob- servations of 20 meteorological v ariables from 1866 ground observation stations across China, spanning from January 2017 to August 2021. W e ha ve selected four surface meteorological variables as the focus of our research, which are: air tempera- ture, air pressure, wind speed, and precipitation in 1 hour . For the downscaling task at the scatter station scale, the primary objectiv e is to v erify the model’ s generalization performance at various scattered locations. Therefore, as shown in Fig. 2, we randomly split the 1866 stations into three non-overlapping parts, with 1266 stations used for training, 200 stations for validation, and the remaining 400 stations used for testing. C. Evaluation Metrics T o e valuate the do wnscaling ef fects of different methods at the scale of scattered observ ation stations, referencing prior work [31], we have chosen the mean squared error (MSE) and mean absolute error (MAE) averaged over both stations and time as our assessment metrics. The calculation methods are as follows: M S E = 1 M ∗ T M X i =1 T X t =1 ( Y t i − ˆ Y t i ) 2 M AE = 1 M ∗ T M X i =1 T X t =1 | Y t i − ˆ Y t i | (2) where M is the total number of test observations, Y t i is the ground truth value for a given variable state at i -th station and t -th time point, ˆ Y t i is the predicted downscaled value. Both metrics are commonly used in regression tasks to measure the accuracy of the predicted v alues. Lower values of MSE and MAE indicate better model performance, with the MAE being particularly useful for understanding the error magnitude on an av erage per-observ ation basis. I V . N E W M E T H O D In response to the downscaling task described above, we dev eloped a nov el method, namely HyperDS , that effecti vely integrates high-resolution Himawari-8 satellite observ ations and scattered station observations to recover subgrid-scale meteorological states from low-resolution atmospheric ﬁelds, achieving continuous-resolution modeling of the meteorolog- ical ﬁeld. This section will provide a detailed introduction to the structure and training strategy of our proposed method. A. Over all Structure The ov erall structure of HyperDS can be viewed as a data- conditional hypernetwork architecture [35]. Considering the type of observ ational data, we use the indirectly observ ed high- resolution Himawari-8 satellite images as auxiliary input to the model, and the direct scattered observation station data as the model’ s station-scale supervision. The reason for this setup is to enable the model to learn the implicit meteorological ﬁeld information from indirect remote sensing observ ations through operations such as encoding and feature extraction of the former . At the same time, supervision from the observation stations is used to correct the inherent biases that occur when downscaling from grid scale to station scale. As illustrated in Fig. 3, our model is composed of three sub-network structures: a dual-branch feature encoder based on CNN and an implicit in version network based on a T rans- former with cross-attention form the hypernetwork, which generates the fused features used to determine the weights of the target network; the target network, in turn, comprises an MLP-based decoder that learns the mapping from speciﬁc co- ordinates to meteorological states, using the weight parameters generated by the hypernetwork. Additionally , in the input portion of the MLP decoder , we design a coordinate selection method based on subgrid sampling that more naturally and reasonably adapts to the capability of implicit neural representation for continuous state modeling. In such a case, by averaging the subgrid samples pixel by pix el, we can utilize high-resolution grid scale data for supervision and learn the deviation loss between the predicted values and the site-scale observations by sampling speciﬁc scatter station locations. A v eraging and sampling of this form are also better aligned with the processing methods used to integrate multiscale observ ational data in meteorological ﬁelds. B. Dual-Br anched F eatur e Encoder For processing meteorological ﬁeld data and satellite im- agery simultaneously , we implemented a simple dual-branch encoding structure based on ResNet-18 [58] as the backbone for both the meteorological ﬁeld encoder and the satellite image encoder . For the satellite image encoding branch specif- ically , we chose to input two adjacent Himawari-8 images in a siamese conﬁguration into the encoder . The rationale behind this approach is inspired by previous work that utilized multi- frame images to infer wind ﬁelds by tracking cloud mov ements [59], with the hope that the model will autonomously learn the features of the two frames and some implicit gradient information. T o balance the semantic information and spatial information of the features, we selected the features from the intermediate layers of the two encoders as the outputs of the model. Speciﬁcally: giv en the low-resolution meteorological JOURNAL OF L A T E X CLASS FILES, VOL. 14, NO. 8, A UGUST 2021 7 I n p u t C o o r d i n a t e Station Point Inner Point Subgrid Sample Input Coordinate          HR Satellite Images           Siamese Image Encoder       Self-Attention Trasnformer Encoder Im p l i c i t Ret r i ev al Net w o r k Cross-Attention Trasnformer Decoder     LR Weather Fields Meteorological Fields Encoder   UP          Du al -B r an c hed Fea t u r e En c o d er Fused Features FC-based Weight Generator ML P Dec o d er Continuous Meteorological Fields Result Mu l t i -s c ale Su per v i s i o n   Grid Mean Station Sample Fig. 3. The proposed HyperDS architecture. It mainly consists of three parts: a dual-branch feature encoder is used to extract semantic features from the input low-resolution meteorological ﬁeld and high-resolution remote sensing images respectively; subsequently , the implicit retrieval network utilizes a cross-attention mechanism to implicitly fuse different feature information and align the remote sensing image features with meteorological ﬁeld variables; and ﬁnally , the FC (fully connected)-based weight generator predicts the weight vector for the target network. The MLP (Multi-Layer Perceptron) decoder , the target network, learns the mapping from the sampled subgrid coordinates to the corresponding location state v alues. It is supervised at both the observ ation station scale and the high-resolution grid scale, allowing for the continuous modeling of the meteorological ﬁelds. F input ∈ R 1 × 5 × LH × LH and two frames high-resolution Himawari-8 remote sensing images O ∈ R 2 × 4 × T H × T W , the extracted features from each encoder can be computed by: F f ield = Con v2d ﬁeld (MeteoEnco der( F input )) F f ield = Con v2d ﬁeld ( F f ield ) F h 8 = Concat(ImgEnco der( O 0 ) , ImgEnco der( O 1 ) F h 8 = Con v2d ﬁeld ( F h 8 ) (3) The two features are e xtracted from the same stage in ResNet- 18 and aligned across all dimensions into C × h × w through upsampling and con volution operations. C. Implicit Retrieval Network T o further integrate the two types of extracted features, we adopted a T ransformer encoder-decoder network based on a cross-attention mechanism. This network implicitly retriev es indirect observ ation information into the meteorological ﬁeld domain and effecti vely integrates it. W e ﬁrst ﬂatten F f ield and F h 8 into shape C × hw , and add the learnable positional encoding vector . Then, the features from high-resolution re- mote sensing images are fed to the self-attention Transformer encoder to further learn the relationships between different tokens. Follo wing a cross-attention Transformer decoder re- ceiv es features from both remote sensing images and mete- orological ﬁelds to implicitly learn the relationships between different feature domains. Therefore, the fused features gen- erated by the implicit retriev al network can be computed by: F h 8 = selfA ttnEnco der( F h 8 ) F f used = crossA ttnDeco der( F h 8 , F f ield ) (4) Through the abov e calculations, the generated fusion features contain high semantic features of both lo w-resolution meteoro- logical ﬁelds and high-resolution satellite observations, laying the foundation for subsequent continuous-resolution modeling. D. MLP Decoder with Subgrid-sampling Based on the fusion features generated by the super network structure and combined with the latent neural representation method [34], we designed a decoder module based on the Multilayer Perceptron (MLP). By learning the mapping from coordinate positions to meteorological states, we realized continuous modeling of the meteorological ﬁeld. Unlike pre vious modeling methods based on latent neural representations that directly use the coordinates of the grid center to represent grid values [38], [48], we designed a specialized sub-grid sampling method speciﬁcally for mete- orological ﬁelds. This allows us to construct a continuous representation of the meteorological ﬁeld more naturally and reasonably . Speciﬁcally , for a gi ven pix el p in a high-resolution grid Grid(TH , TW) , we randomly sample multiple inner points I p = { ( x i , y i ) | i = 1 , 2 , · · · , P } within this pixel as JOURNAL OF L A T E X CLASS FILES, VOL. 14, NO. 8, A UGUST 2021 8     ×   -Net  -Net  -Net  -Net  -Net Generated Fusion Features Linear Generated Fusion Features Linear   Generated Weights Trainable Weights (a) Multi-block-based MLP decoder (b) Multi-variable-based MLP decoder Subgrid Sample Input Coordinate Subgrid Sample Input Coordinate Fig. 4. T wo variants of MLP decoders based on implicit neural representations with subgrid sampling. the coordinate v alues to be input in this pixel. Then, we can obtain the state value for the corresponding resolution grid by calculating the average of the meteorological state v alues associated with all the inner points under that pixel, which can then be supervised using the corresponding high-resolution grid labels. Speciﬁcally , when a pixel includes the location of observation stations, we will also sample the positions of these observ ation stations. By using proposed the subgrid sampling method described above, we can average the data from observ ation stations into the mean v alue of the grid, thereby mitigating the conﬂict between the scattered point stations and the grid values. It should be noted additionally that, apart from the coordinate values, we also input the grid interpolation results of the state values corresponding to the coordinate points as auxiliary information into the MLP . For the sake of simplifying the expression, this part of the information will not be explicitly reﬂected in the following text. As for the MLP modeling method used to represent the meteorological ﬁeld, as shown in Fig. 4, we referenced previous work [60] and designed two different modeling structures. The ﬁrst type, the multi-block-based MLP decoder , divides the tar get meteorological ﬁeld into sev eral blocks, each of which is continuously modeled by a separate MLP that takes input coordinates and simultaneously outputs the state values of all target v ariables. The weights of the network are obtained entirely through the linear mapping of fused features. Different from the ﬁrst one, the second type is a multiv ariate MLP decoder that uses different MLPs to model the entire meteorological ﬁeld of speciﬁc variables separately . The shallow parameters of each MLP are obtained through linear mapping of the fused features, whereas the deeper parameters are randomly initialized and constitute learnable weights. The reason for this setup is that the former , multi- block-based modeling approach, although more conduci ve to modeling high-frequency information, is more memory- intensiv e and increases model complexity with the number of sub-blocks. The latter has a relativ ely ﬁxed computational complexity and memory usage, but it makes the modeling task more challenging for a single MLP . Therefore, each method has its advantages and disadvantages, and we hope to provide more ﬂexible options for our approach. E. Loss Function The supervision label data proposed for HyperDS includes two scales: grid-scale and station-scale. By inputting different sampling coordinates into the MLP decoder , predictions for the corresponding scales can be generated. Detailed introductions follow . 1) Grid-scale Loss: Referencing previous downscaling work based on Super-Resolution (SR), we use high-resolution meteorological ﬁelds as supervision at the grid scale. Ho we ver , unlike previous work, we obtain the prediction result for a target pixel by calculating the average of the sub-grid inner points within that pixel. T o be speciﬁc, gi ven the high- resolution grid label ﬁeld F g r id label ∈ R 1 × 5 × T H × T W , we sample P inner points I p = { ( x i , y i ) | i = 1 , 2 , · · · , P } at each pixel p in Grid(TH , TW) and the predicted ﬁeld can be computed by: F g r id output = 1 P P X i =1 mlpDeco der( I , F f used ) (5) then, the grid-scale loss can be computed by: L g r id = ∥F g r id label − F g r id output ∥ 2 (6) Howe ver , while high-resolution supervision can provide ac- curate mean supervision on ﬁne grids, in actual applications, high-resolution grid supervision is often difﬁcult to obtain. T o account for station-scale downscaling in such situations, we referenced previous work on modeling dynamic systems [61] and designed a grid loss function for when high-resolution gridded supervision is not available. In such cases, still ben- eﬁting from the sub-grid sampling coordinate input form, we could also compute the mean v alues cov ered by the low- resolution pixel in Grid(LH , L W) , at the same time interpolate the input low-resolution ﬁelds into a ﬁne-grained one. Thereby simultaneously obtaining the interpolated high-resolution su- pervision as well as the lo w-resolution mean supervision: L H R = ∥ In terp( F input ) − F g r id output ∥ 2 L LR = ∥F input − Avgp o ol( F g r id output ) ∥ 2 L g r id = L H R + L LR (7) Through such an approach, in the absence of high-resolution grid supervision information, it is possible to provide as much JOURNAL OF L A T E X CLASS FILES, VOL. 14, NO. 8, A UGUST 2021 9 grid supervision information as possible to the maximum extent. 2) Station-scale Loss: T o integrate the observational infor- mation from scattered stations into the do wnscaling process and mitigate the inherent bias between the meteorological ﬁeld and grid observations, the training process incorporates station-scale supervision to learn the cross-scale mapping from the meteorological ﬁeld to the stations. T o be speciﬁc, gi ven the station-scale label F station label ∈ R 1 × 5 × M , where M is the number of stations, we could sample the corresponding coordinates and computed the station scale output by: F station output = mlpDeco der( I ′ , F f used ) (8) and the station-scale loss is L stn = ∥F station label − F station output ∥ 2 (9) It should be noted that since only the wind speed variable, rather than its components, is provided in the W eather2K data [33], we base our calculation of wind speed loss on the following formula: w ind speed = q u 2 10 + v 2 10 . (10) Combining the abov e loss functions, we can deriv e the ﬁnal loss function as: L = L g r id + β L stn (11) where β are the loss coefﬁcients that need to be manually set. V . R E S U LT S In this section, we design experiments and baseline methods tailored to the downscaling task we have constructed, which will be compared with our proposed HyperDS model. A. Experiment Details T o validate the downscaling performance from lo w- resolution meteorological ﬁelds to arbitrary scatter stations, we downsampled the original ERA5 reanalysis data [30] to a spatial resolution of 1 ◦ using the method of av erage pooling, which served as the input meteorological ﬁeld data. Moreover , we used the original ERA5 data at 0 . 25 ◦ resolution as high- resolution grid supervision. Additionally , we conducted exper- iments without high-resolution grid supervision by setting the loss according to Eq. 7. The dataset was di vided into three parts in chronological order: data from January 1, 2017, to August 31, 2020, was used for training; data from September 1, 2020, to December 31, 2020, was used for validation; and data from January 1, 2021, to August 31, 2021, was utilized for testing. It should be noted that for the observational station data from W eather2K [33], we partitioned the dataset based on both time and station locations. This division requires that the model exhibit strong generalization performance both temporally and spatially when validated at the observational station scale, which presents a signiﬁcant challenge. Therefore, the experiments we set up aim to recover the meteorological state v ariables at a scatter scale from a 1 ◦ spatial resolution meteorological ﬁeld and to validate the performance at 400 randomly sampled test stations (as shown in Fig. 2) within the testing period. The hyperparameter number of samples in the MLP decoder is set to 10, and the loss coefﬁcient β = 0 . 05 . T o ensure a fair comparison of different methods, we hav e established the same training procedures and hyperparameters for all. W e optimized the model using the Adam optimization method [62], employing a cyclical learning rate with cosine annealing [63], starting with an initial learning rate of 0.0001, for a total of 50 epochs of training. W e choose the checkpoint with the lowest station-level loss in the validation sets for testing. W e trained our proposed model using 4x NVIDIA A100 GPUs, setting the batch size to 4 per GPU. B. Baselines For the benchmark we proposed, we designed two basic baseline methods for comparison to validate the effecti veness of our method. The following subsections provide a detailed introduction to these methods. 1) Interpolation of W eather F ield into Station Scale: One of the simplest and most direct methods to obtain meteoro- logical state variables at the scale of scattered stations from a meteorological ﬁeld is through interpolation. W e use the DataArra y . in terp function with the default setting from the open-source xarra y library to perform interpolation on the meteorological ﬁeld, based directly on the absolute positions of latitude and longitude, with each grid cell’ s state v alue corresponding to its center point coordinates. W e mainly per- formed interpolation on meteorological ﬁelds with resolutions of 1 ◦ and 0 . 25 ◦ , corresponding to the interpolated results from the input low-resolution meteorological ﬁelds and the high- resolution supervision. Since the interpolation process does not incorporate any av ailable observational information, this method can serve as our most basic baseline result. Moreover , it can reﬂect to some extent the inherent bias that exists between the meteorological ﬁelds and observ ations. 2) Super -Resolution-based Downscaling with Observa- tions: Giv en the widespread application of super-resolution models in downscaling tasks, we speciﬁcally modiﬁed tradi- tional super-resolution models for our proposed benchmark, integrating multi-scale observ ational information into them. As shown in Fig. 1(a), traditional SR-based do wnscaling methods mainly learn the mapping between low-resolution input ﬁelds and the target high-resolution ﬁelds within an encoder-decoder architecture. W e adopted a straightforward approach to in- corporate high-resolution Himawari-8 (H8) satellite imagery observations and W eather2K station observations into the model. Speciﬁcally , given the high-resolution H8 images we encode them with a single con volutional layer , then align the dimension with the input meteorological ﬁelds by av erage pooling operation and concatenated them on top of the input low-resolution meteorological ﬁeld before feeding them into the super-resolution model. After obtaining the meteorological ﬁeld at the target resolution, the meteorological state of the scattered stations can be acquired through interpolation. Sub- sequently , both the grid supervision and the corresponding sta- tion supervision data are utilized to compute the loss function, which is then used for backpropagation. In terms of the choice JOURNAL OF L A T E X CLASS FILES, VOL. 14, NO. 8, A UGUST 2021 10 T ABLE III S TA T I ON - L E VE L D O W N S C A LI N G R ES U LTS F O R W I N D S P EE D ( w s ) , S UR FAC E PR ES S U R E ( sp ) , 2 M T E MP E R ATU R E ( t 2 m ) A ND TO TA L P R E C IP ITA T IO N I N 1 H O UR ( tp 1 h ) O F V A R IO US M E T HO D S . Method w s sp t 2 m tp 1 h MSE MAE MSE MAE MSE MAE MSE MAE ERA5 1 ◦ 5.5642 1.7842 1048.3886 21.1125 7.7483 1.9235 1.1396 0.1896 ERA5 0 . 25 ◦ 6.2164 1.9118 801.3915 17.2155 6.7855 1.7770 1.2018 0.1893 UNet [64] 5.4575 1.7757 967.8221 20.1538 7.3537 1.8806 1.1426 0.1955 EDSR [42] 6.1547 1.8905 896.9313 19.2898 7.1336 1.8386 1.1572 0.1982 HyperDS (Ours, multi-var) 1.7995 0.9568 716.0126 15.4001 6.3588 1.7656 1.1278 0.1887 HyperDS (Ours, multi-block) 1.9671 1.0126 645.0722 14.6524 6.5747 1.8400 1.1260 0.1859 of super -resolution models, we selected the classic UNet-based super-resolution model [64] and the EDSR [42] and made modiﬁcations to their structures and implementations. C. Comparison with Baselines W e compared the performance of our proposed HyperDS method with other baseline methods for station-scale do wn- scaling with high-resolution grid supervision. Due to the trade- off between grid-scale supervision and station-scale supervi- sion in the model optimization process, but as our current task mainly focuses on the performance at the station scale, we chose the checkpoint with the smallest station-scale loss on the v alidation set during the training process as the model for testing. The loss coefﬁcients can also greatly affect site performance, so considering the need to balance the losses at both scales, we empirically set the loss coefﬁcients in Eq. 11 as β = 0 . 05 . Subsequent sections will further discuss the trade-off problem between the losses at the two scales. Since the W eather2K dataset [33] used as labels do not include the wind speed component, we compared the downscaling results of 4 surface variables, which are: wind speed ( w s ), surface pressure ( sp ), 2m temperature ( t 2 m ) and total precipitation in 1 hour ( tp 1 h ). 1) T est Results by V ariables: T ab . III displays the test metrics for different v ariables using different methods at the 400 testing observation stations. From the results, it can be seen that our proposed HyperDS method outperforms the compared baseline methods on all variables. Particularly for wind speed and surface pressure, our method signiﬁcantly exceeds the others, with the MSE for wind speed improving by 67% and for surface pressure by 19.5% compared to the best baseline results. It should be noted that in the results of direct interpolation of meteorological ﬁelds, the ERA5 1 ◦ interpolation results are superior to the 0 . 25 ◦ interpolation results in metrics such as wind speed and precipitation, which seems counterintuitiv e. Howe ver , similar results hav e been reported in recent related work [31]. W e believe this is due to the limited assimilation of observational station data in the ECMWF reanalysis data for the China region. Upon further analysis of the test results for different v ari- ables, it is evident that our method sho ws the most signiﬁcant improv ement in wind speed. This is primarily because wind speed exhibits the most notable sub-grid variability , with local wind speeds often being inﬂuenced by a v ariety of small-scale meteorological processes such as turbulence, making it difﬁ- cult to capture at the relatively coarse resolution of grid scales. On the contrary , for variables such as 2m temperature and precipitation, the improvement from our method is relativ ely small. This is because the v ariability of local temperature is relativ ely gradual, and as for precipitation, due to its sparse and long-tailed distrib ution [65], acceptable do wnscaling results can be obtained by simply interpolating the grid data. For the two super-resolution-based comparison methods, we can see that although observational information has been incorporated, the improv ement in ov erall station downscaling performance is quite limited. W e believ e that this is be- cause traditional super-resolution methods, which are based on ﬁxed-resolution grid supervision, place more emphasis on the regression task for each grid pixel, and the learning process remains a discrete mapping from coarse grid scales to ﬁne grid scales. In contrast, the optimization goal of our proposed HyperDS method, which is based on hypernetworks and implicit neural representations, is to learn a mapping from arbitrary coordinates to meteorological states, constructing a continuous representation of the meteorological ﬁeld. This endows the model with stronger capabilities for expressing sub-grid-scale information. This also explains why the EDSR model, which has stronger grid super-resolution capabilities, performs worse in station do wnscaling than the simpler UNet model. The reason is that EDSR has a stronger ability to fuse and extract features at the grid scale, which makes it difﬁcult for the model to generalize well to the station scale, e ven with the inclusion of station-scale observations as supervisory labels. For the two dif ferent MLP decoder structures we proposed, it can be seen that dif ferent decoder outcomes ha ve certain per - formance differences for different v ariables. The multi variate- based HyperDS performs relativ ely better on wind speed and 2m temperature, while the multi-block-based HyperDS performs better on surface pressure and precipitation. W e JOURNAL OF L A T E X CLASS FILES, VOL. 14, NO. 8, A UGUST 2021 11 believ e this is due to the different statistical distributions of various v ariables. Although we have normalized all variables by their mean and variance, making them roughly follow a Gaussian distribution with zero mean, there are still signif- icant differences in the value ranges of each variable after normalization. For example, the v ariation range of surface air pressure is relati vely lar ger, whereas the temperature variation range is comparatively smaller . The decoder based on multiple blocks, with each MLP representing a local region, can model the data for a speciﬁc area more ef fecti vely , thus av oiding the issue of too great a range of variable changes caused by global modeling. The decoder based on multiple variables uses a single MLP to model the entire meteorological ﬁeld of a region, which is more effectiv e for variables with smaller ranges of v ariation and can also sav e more computational memory consumption. 2) Result V isualization: Fig. 5 illustrates the results of downscaling at different test stations using v arious methods, where the color of each station represents the magnitude of the normalized mean square error at that station, with lighter colors indicating larger errors. The base map of each visual image is also the result of downscaling at the grid scale with 0 . 25 ◦ spatial resolution of each model. The results in the ﬁgure show that our proposed HyperSR method performs signiﬁcantly better at the site scale compared to other methods. In particular , for the wind speed variable, the baseline methods exhibit a lar ge error in the northeastern area of the study re gion (more white dots), but our method can ef fectiv ely correct the downscaling bias in this area. Combining this with Fig. 2, we can see that for areas with sparser training stations (such as the northeastern and western regions), the downscaling performance of all methods tends to decline to dif ferent extents compared to the densely observed southeastern re- gion. Howe ver , our method still exhibits better generalization performance; for instance, for the 2m temperature variable, our method has relatively fewer white dots in the northeastern region compared to other baseline methods. It is note worthy that the downscaling method based on super-resolution (SR) achiev es better do wnscaling results at the grid scale (i.e., base map) compared to our method. This is a limitation of our method and a direction for further improv ement in the future. D. Downscaling without High-r esolution Gridded Supervision In practical applications, high-resolution gridded meteo- rological ﬁelds are often difﬁcult to obtain, whereas direct observations at observ ation stations are relatively easier to access and the data quality is more stable. Obtaining station- scale meteorological states directly from low-resolution meteo- rological ﬁelds is a very meaningful task. Hence, we conducted station-scale downscaling experiments without high-resolution grid supervision based on the designed loss function Eq. 7. T ab . IV shows the downscaling results at the station level for different methods. The results from the table indicate that, ev en without high-resolution grid supervision, our proposed HyperDS outperforms other methods on the majority of the ev aluation metrics for most variables, particularly for the wind speed variable. Ho wev er , for 2m-temperature and surface pres- sure v ariables, compared to the results supervised with high- resolution grid data, there is a noticeable performance decrease (for surface pressure, the MSE decreased from 645.0722 to 805.9112, and for 2m-temperature, it decreased from 6.3588 to 7.1487). This performance de gradation is because high- resolution grid supervision provides a signiﬁcant improvement ov er coarse-resolution grid inputs at the station lev el for these two variables. Consequently , the absence of high-resolution grid data supervision leads to a decline in performance. In contrast, for the wind speed v ariable, the downscaling performance at the station lev el is slightly improved (MSE decreased from 1.7995 to 1.7815) because the interpolation results from lo w-resolution inputs are less dependent on high- resolution supervision. Although there is a certain degree of performance decline, our proposed HyperDS method still outperforms the com- parison methods e ven without high-resolution grid supervi- sion. Even when the comparison methods incorporate high- resolution supervision (as shown in the results of T ab. III), our method remains superior on most metrics compared to those based on grid super-resolution networks. E. Ablation Study W e further compared the performance of the HyperDS method under different settings to verify the impact of the inclusion of observ ational data and the number of samples on the method’ s performance. T ab . V shows the test performance of HyperDS under different experimental settings. The results indicate that the inclusion of station observation supervision is the most critical factor affecting the model’ s performance. This is intuiti ve, as previous work has also shown that there is an inherent bias between the meteorology itself and scatter station observations [31], which cannot be reco vered solely through high-resolution grid supervision. Based on this result, coupled with the fact that we use station observations as our supervision labels, it means that no real-time station observations are needed during the model inference stage. The model itself can adaptively generalize the meteorological ﬁeld to any station location, which also implies that the model has learned the inherent bias from the meteorological ﬁeld to the station and has effecti vely reduced it. Therefore, our method can be regarded as a general interpolation model from the meteorological ﬁeld to stations. Regarding the input of H8 remote sensing satellite images, although it is not a dire ct representation of meteorological con- ditions, through our designed feature extraction and implicit retriev al network, the model can learn useful information from indirect observations. Howe ver , the results indicate that the input from H8 did not sho w a positive impact on all variables. This is because the satellite observations we input are Lev el 1 radiance data, in which the meteorological state information is implicit and incomplete. From the types of Lev el 2 (L2) in version products provided by the Himawari-8 satellite, it is evident that the primary meteorological variables related to it are surface temperature, humidity , and high-altitude wind speed (obtained indirectly based on cloud movement). There- fore, in the experimental results, the incorporation of H8 data JOURNAL OF L A T E X CLASS FILES, VOL. 14, NO. 8, A UGUST 2021 12 surface pressure 2m te mperatur e wind speed total pre cipitation ERA5 1 ° ERA5 0.25 ° UNet EDSR Ours multi-var Ours multi-block Fig. 5. V isualization comparison of downscaling to station-scale using different methods, where the color of each station represents the magnitude of the normalized mean square error at that station, with lighter colors indicating larger errors, i.e. the darker the color of the site, the better the performance of the downscaling. The base map of each visual image is also the result of downscaling at the grid scale with 0 . 25 ◦ spatial resolution of each model. JOURNAL OF L A T E X CLASS FILES, VOL. 14, NO. 8, A UGUST 2021 13 T ABLE IV S TA T I ON - L E VE L D O W N S C A LI N G R ES U LTS F O R W I N D S P EE D ( w s ) , S UR FAC E PR ES S U R E ( sp ) , 2 M T E MP E R ATU R E ( t 2 m ) A ND TO TA L P R E C IP ITA T IO N I N 1 H O UR ( tp 1 h ) O F V A R IO US M E T HO D S W I T H OU T H I GH - R E SO LU T I O N G R ID DE D S U PE RVI SI O N . Method ws sp t 2 m tp 1 h MSE MAE MSE MAE MSE MAE MSE MAE UNet [64] 5.3051 1.7508 1078.9179 21.6993 7.6797 1.9225 1.1426 0.1992 EDSR [42] 5.2994 1.7495 1082.5246 21.7704 7.6539 1.9183 1.1426 0.1902 HyperDS (Ours, multi-var) 1.7815 0.9613 901.4435 17.9062 7.1487 1.8239 1.1319 0.1940 HyperDS (Ours, multi-block) 2.0379 1.0335 805.9112 16.0210 7.4909 1.9281 1.1274 0.1943 T ABLE V A B LAT I O N S T UDY R E S ULT S O F H Y P E R D S W I T H M U LT I - B L O CK - BA SE D M L P D E CO D E R . T H E S ET T I N GS ’ S TA T I O N ’ A N D ’ H 8 ’ R EP R E S EN T T H E S TA T I ON - L E VE L S U PE R V IS I O N AN D H 8 S A T EL LI T E I M AG ES I N P UT . T H E S E TT I N G ’ S A M P LE ’ R E PR E S E NT S T H E S U BG RI D - S AM P L I NG S T R A T E G Y I N M L P D E CO DE R . Method Settings ws sp t 2 m tp 1 h station h8 sample MSE MAE MSE MAE MSE MAE MSE MAE HyperDS ✗ ✓ ✓ 5.4509 1.7769 1088.7840 23.3697 9.2645 2.2367 1.1427 0.1983 ✓ ✗ ✓ 1.8876 0.9893 721.9860 15.2776 6.8517 1.8417 1.1262 0.1910 ✓ ✓ ✗ 2.3029 1.1133 729.5865 15.7978 7.1172 1.8925 1.1322 0.1936 ✓ ✓ ✓ 1.9671 1.0126 645.0722 14.6524 6.5747 1.8400 1.1260 0.1859 has a more pronounced improvement in 2m temperature and surface pressure (which are strongly correlated with humidity). Howe ver , for the surface wind speed, since it has a signiﬁcant deviation from the high-altitude wind speed, the results do not show a direct enhancement. Sampling at the subgrid coordinates is also one of the innov ativ e aspects of our method. By using subgrid sampling, the traditional implicit neural representation methods can be better aligned with the continuous distribution characteristics of the meteorological ﬁeld, and the scattered station observ a- tions are treated as samples to be a veraged with other samples within the same pix el. W e conﬁgured various subgrid sampling numbers for comparison, and the experimental results also indicate that more samples typically yield better experimental outcomes and faster con v ergence rates. Howe ver , excessi ve sampling usually means greater GPU memory usage; there- fore, we only set the maximum number of samples to 10 during the experimental process. F . Optimization process analysis Since our method requires the simultaneous optimization of two losses at the grid scale and the station scale, we further discuss the trade-of f between these two types of losses to analyze the impact of dif ferent losses and labels on the model optimization process. Both pre vious work [31] and the exper - imental results discussed above hav e adequately illustrated a substantial systematic bias between meteorological conditions at the station scale and the grid scale. Our approach uses the meteorological ﬁelds at the grid scale as input and, by modeling a continuous representation of the meteorological ﬁeld, aims to obtain high-precision meteorological states at the station scale to alle viate this systematic bias. Ho wev er, during the training process, as mentioned in Eq. 11, we introduced supervisory information from both the station scale and the grid scale and combined them in a weighted sum to serve as the objectiv e function. This also creates a trade-off between the two different losses. Fig. 6 displays the changes in the normalized MSE loss for the validation set at both the station-scale and grid scale during the training process. It should be noted that because we have incorporated strong prior information (such as interpolation results, etc.) as inputs into our model, the model is capable of achieving satisfactory con vergence within just one epoch. As a result, the overall loss function appears relativ ely smooth. The curves in the ﬁgure indicate that for all models, the grid- scale loss decreases steadily with the progression of training. Howe ver , the station-scale loss is relativ ely more volatile and tends to ﬁrst decrease and then increase as the number of training epochs increases (this is particularly evident for the models with β = 0 . 05 ). As β increases from 0.05 to 0.1, this phenomenon is somewhat mitigated, but there is a corresponding decline in performance at the grid scale. W e believ e that such results are primarily due to a certain lev el of discrepancy between the two types of losses, and the fact that there are fewer station-scale samples compared to grid-scale samples, leading to a degree of sample imbalance. Furthermore, the results in the table also re veal that high- resolution grid supervision has a signiﬁcant impact on grid- scale performance, b ut the ef fect is relati vely tolerable for station-scale predictions. Upon further analysis of cases with high-resolution station supervision, models with multi-block decoders exhibit a signiﬁcant performance improvement at JOURNAL OF L A T E X CLASS FILES, VOL. 14, NO. 8, A UGUST 2021 14 (a) Normalized MSE va lidation loss on station-level scale. (b) Normalized MSE va lidation loss on grid-level scale. Fig. 6. Illustration of the changes in the normalized MSE loss on the validation set under various hyperparameter settings during the training process, with 0.05 and 0.1 indicating the γ values of the station loss in Eq. 11. the grid scale compared to multi-variable decoders; howe ver , this improvement is not as pronounced at the station scale. Additionally , the con ver gence speed of the former is noticeably superior to that of the latter . From the analysis above, it is e vident that for the novel benchmark we proposed, it is unreasonable to focus solely on improving station-scale performance without considering the grid scale. Therefore, devising more rational model structures to further enhance the downscaling performance at both scales is an important research direction for the future. V I . D I S C U S S I O N The purpose of this paper is to do wnscale grid-scale meteo- rological ﬁeld data to the scale of discrete scatter stations. This allows us to obtain the meteorological state at any location based on widely used coarse-resolution meteorological ﬁeld data, which has signiﬁcant practical importance. The bench- mark proposed in this paper , along with the novel method HyperDS, integrates multi-scale observ ational information into the do wnscaling task, effecti vely achie ving station-scale do wn- scaling. Ho wev er , there are still man y aspects of this task that can be further explored and researched. W e will discuss the current issues and potential future directions from tw o perspectiv es: the data and the methodology . 1) Observation Data: Based on the experiments and anal- yses conducted, it is evident that incorporating multi-scale observational data plays a crucial role in the downscaling task. The dataset we currently propose includes only two types of observ ational information: station observ ations and geo- stationary satellite radiance v alues. Especially with regard to satellite observations, the data types contained within a single data source are quite limited. In the operational forecasting data assimilation process [51], multisource and multisensor remote sensing data are used to obtain different meteorological variables. Therefore, integrating more types of remote sensing observation data into the dataset is important for constructing a continuous-scale multi variate meteorological ﬁeld. Howe ver , this task is also very challenging, in volving specialized knowl- edge related to the sensors and corresponding meteorological variables, as well as complex data preprocessing procedures. In addition, the number of station data points we utilized is still relatively small. Previous work has used data from tens of thousands of stations to achie ve high-accuracy station-scale weather forecasts [31]. Incorporating more station data is also crucial for continuous-scale modeling. W e also welcome more researchers to integrate more types of data into our benchmark to enhance the capability of continuous-scale modeling for more meteorological variables, and we hope that related work can assist with the practical applications of meteorological forecasting. 2) Models and Methodology: Designing model architec- tures and methods suitable for the current task is also key to improving the performance of the benchmark. Unlike tra- ditional downscaling works based on super-resolution, do wn- scaling to the scale of individual stations places higher de- mands on the model’ s ability to represent resolution contin- uously . The HyperDS proposed in this paper starts from this perspectiv e and has achie ved good performance in downscal- ing to the station scale. Howe ver , the current method sacriﬁces the performance of grid-scale do wnscaling to some extent in order to enhance station-scale do wnscaling, which is not a trade-off we desire to see. This is also a common problem with many super-resolution methods based on implicit neural rep- resentations. Therefore, ho w to design a more effecti ve model that ensures multi-scale modeling accuracy while supporting continuous-resolution representation is an urgent issue to be addressed in the future. V I I . C O N C L U S I O N In this paper, we extend the traditional ﬁxed-resolution grid-based do wnscaling task to the scale of scattered station scale, based on the characteristics of meteorological vari- ables. Inspired by data assimilation [51], we integrate multi- scale observational data into the do wnscaling process and build a novel benchmark and dataset that downscales coarse- resolution meteorological ﬁelds to station scales. Building on this foundation, we propose a new model based on a h y- pernetwork structure called HyperDS . It uses high-resolution remote sensing images as prior input and scattered observation station data as station-scale labels. By continuously model- ing the meteorological ﬁeld, it effecti vely inte grates multi- scale observ ational information and achie ves high-precision JOURNAL OF L A T E X CLASS FILES, VOL. 14, NO. 8, A UGUST 2021 15 meteorological ﬁeld downscaling at the station scale. Through extensi ve experimental comparisons with specially designed baseline methods, we have veriﬁed the ef fectiv eness of our proposed approach, particularly in terms of performance on wind speed and surface pressure variables, where it sig- niﬁcantly outperforms other methods. This paper represents the ﬁrst exploration into observ ation-driv en do wnscaling of meteorological ﬁelds to station scales. W e hope that in the future, more researchers will build on this foundation to study more effecti ve methods, enhancing the accuracy and capability of continuous meteorological ﬁeld modeling. R E F E R E N C E S [1] X. Ren, X. Li, K. Ren, J. Song, Z. Xu, K. Deng, and X. 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Observation-Guided Meteorological Field Downscaling at Station Scale: A Benchmark and a New Method

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