In current many years, international local weather monitoring has made vital strides, resulting in the creation of latest, in depth observational datasets (Karpatne et al., 2019). These datasets are important for bettering numerical climate predictions and refining distant sensing retrievals by offering detailed insights into advanced bodily processes (Alizadeh, 2022). Nonetheless, as the amount and complexity of the information grows, figuring out patterns throughout the observations turns into more and more difficult (Zhou et al., 2021). Extracting key options from these datasets might result in vital developments in our understanding of phenomena like convection and precipitation, additional enhancing our information of the altering international local weather.
On this submit, we are going to discover a few of these advanced information patterns via the lens of precipitation, which has been highlighted as a critically vital space of examine beneath warming international temperatures (IPCC, 2023). Slightly than counting on randomly generated or simulated information for this undertaking, we are going to work with real-world observations from throughout the globe, that are publicly accessible for you, my reader, to discover and experiment with as effectively. Let this submit function a analysis information, beginning with the significance of fine high quality information, and concluding with insights on linear and nonlinear interpretations of mentioned information.
When you’d prefer to comply with together with some code, try our interactive Google Colab pocket book.
This evaluation unfolds in three elements, every of which is a separate, printed analysis article:
- Curating a strong, multidimensional dataset
- Analyzing linear embeddings
- Exploring nonlinear options
1. The Microphysical Dataset
https://doi.org/10.1029/2024EA003538
Once we speak about understanding the options of precipitation, what are we actually asking? How advanced can one thing as frequent as rain or snow be? It’s simple to look exterior on a stormy day and say, “It’s raining” or “It’s snowing”. However what’s really occurring in these moments? Can we be extra exact? For instance, how intense is the rainfall? Are the raindrops giant or small? If it’s snowing, what do the snowflakes seem like ? Are they fluffy, dendritic crystals, or are they composed of a number of, fused particles in giant mixture clumps (e.g., Fig. 1)? If the temperature hovers close to zero levels Celsius (C), do the snowflakes turn into dense and slushy? How briskly are they falling? These variations might have a huge impact on what occurs when the particles attain the bottom, and categorizing these processes into distinct teams is non-trivial (Pettersen et al., 2021).
Understanding these processes is essential for higher monitoring and mitigating the impacts of flooding, runoff, freezing rain and excessive precipitation, all of that are doubtlessly harmful occasions with billions of {dollars} of related international damages every year (Sturm et al., 2017). However with 1000’s of particles falling over only a few sq. meters in a matter of minutes, how can we quantify this advanced course of? It’s not nearly counting the particles, we additionally have to seize key traits like dimension and form. As a substitute of making an attempt this manually (an unimaginable job, go attempt for your self), we usually depend on distant sensing devices to do the heavy lifting. One such instrument is the NASA Precipitation Imaging Bundle (PIP), a video disdrometer that gives detailed observations of falling rain drop and snow particles (Pettersen et al., 2020), as proven beneath in Fig. 2.
This comparatively cheap instrument consists of a 150-watt halogen bulb and a high-speed video digicam (capturing at 380 frames per second) positioned two meters aside (King et al., 2024). As particles fall between the bulb and the digicam, they block the sunshine, creating silhouettes that may be analyzed for variations in dimension and form. By monitoring the identical particle throughout a number of frames, the PIP software program may also decide its fall velocity (Fig. 3). With extra assumptions about particle movement within the air, the PIP information permit us to additionally derive minute-scale particle dimension distributions (PSDs), fall speeds, and efficient particle density distributions (Newman et al., 2009). These microphysical measurements, when mixed with close by meteorological observations of floor variables like temperature, relative humidity, strain, and wind velocity, supply a complete snapshot of the atmosphere on the time of remark.
Over a span of 10 years, we collected greater than 1 million minutes of particle microphysical observations, alongside collocated floor meteorological variables, throughout 10 completely different websites (Fig. 4). Gathering information from a number of regional climates over such a protracted interval was essential to constructing a strong database of precipitation occasions. To make sure consistency, all microphysical observations have been recorded utilizing the identical kind of instrument with similar calibration settings and software program variations. We then carried out an intensive high quality assurance (QA) course of to eradicate faulty information, appropriate timing drifts, and take away any unphysical outliers. This curated info was then standardized, packaged into Community Widespread Information Type (NetCDF) information, and made publicly accessible via the College of Michigan’s DeepBlue information repository.
You’re welcome to obtain and discover the dataset your self! For extra particulars on the websites included, the QA course of, and the microphysical variations noticed between areas, please confer with our related information paper printed within the journal of Earth and House Science.
To explain the PSD, we calculate a pair of parameters (n0, and λ) representing the intercept and slope of an inverse exponential match (Eq. 1). This match was chosen because it has been extensively utilized in earlier literature to precisely describe snowfall PSDs (Cooper et al., 2017; Wooden and L’Ecuyer, 2021). Nonetheless, different suits (e.g., a gamma distribution) is also thought-about in future work to higher seize giant mixture particles (Duffy et al., 2022).
n0-λ joint 2D histograms are proven beneath in Fig. 5 for every website, demonstrating the wide range of precipitation PSDs occurring throughout completely different regional climates. Observe how some websites show bimodal distributions (OLY) evaluate to very slender distributions at others (NSA). We have now additionally put collectively a Python API for interacting with and visualizing this information referred to as pipdb. Please see our documentation on readthedocs for extra info on learn how to set up and use this package deal in your personal undertaking.
In abstract, we’ve compiled a high-quality, multidimensional dataset of precipitation microphysical observations, capturing particulars such because the particle dimension distributions, fall speeds, and efficient densities. These measurements are complemented by a spread of close by floor meteorological variables, offering essential context in regards to the particular forms of precipitation occurring throughout every minute (e.g., was it heat out, or chilly?). A full record of the variables we’ve collected for this undertaking is proven in Desk 1 beneath.
Now, what can we do with this information?
2. Analyzing Linear Embeddings with PCA
https://doi.org/10.1175/JAS-D-24-0076.1
With our information collected, it’s time to place it to make use of. We start by exploring linear embeddings via Principal Element Evaluation (PCA), following the methodology of Dolan et al. (2019). Their work centered on uncovering the latent options in rainfall drop dimension distributions (DSDs), figuring out six key modes of variability linked to the bodily processes that govern drop formation throughout a wide range of areas. Constructing on this, we intention to increase the evaluation to snowfall occasions utilizing our customized dataset from Half 1. I received’t delve into the mechanics of PCA right here, as there are already many wonderful sources on TDS that cowl its implementation intimately.
Earlier than making use of PCA, we section the complete dataset into discrete 5-minute intervals. This segmentation permits us to calculate the PSD parameters with a sufficiently giant pattern dimension. We then filter these intervals, choosing solely these with efficient density values beneath 0.4 g/cm³ (i.e., values usually related to snowfall and characterised by much less dense particles). This filtering ends in a dataset of 210,830 five-minute durations prepared for evaluation. For the variables used to suit the PCA, we select a subset from Desk 1 associated to snowfall, derived from the PIP. These variables embody n0, λ, Fs, Rho, Nt, and Sr (see Desk 1 for particulars). We centered on a smaller subset of observations from the disdrometer alone right here, as a result of future websites won’t have collocated floor variables and we have been enthusiastic about what might be extracted from simply this six-dimensional dataset.
Earlier than diving into the evaluation, it’s vital to first examine the information to make sure every little thing seems as anticipated. Keep in mind the previous GIGO addage, rubbish in, rubbish out. We need to mitigate the affect of dangerous information if we will. By inspecting the worth distributions of every variable, we confirmed they fall throughout the anticipated ranges. Moreover, we reviewed the covariance matrix of the enter variables to achieve some preliminary insights into their joint conduct (Fig. 6). As an illustration, variables like n0 and Nt, each tightly coupled to the variety of particles current, present excessive correlation as anticipated, whereas variables like efficient density (Rho) and Nt show much less of a relationship. After scaling and normalizing the inputs, we proceed by feeding them into scikit-learn’s PCA implementation.
Making use of PCA to the inputs ends in three Empirical Orthogonal Capabilities (EOFs) that collectively account for 95% of the variability within the dataset (Fig. 7). The primary EOF is probably the most vital, capturing roughly 55% of the dataset’s variance, as evidenced by its broad distribution in Fig. 6.a. When inspecting the usual anomalies of the EOF values for every enter variable, EOF1 exhibits a powerful damaging relationship with all inputs. The second EOF accounts for about 20% of the variance, with a barely narrower distribution (Fig. 6.b) and is most strongly related to the Fallspeed and Rho (density) inputs. Lastly, EOF3, which explains round 15% of the variance, is primarily associated to λ and snowfall fee variables (Fig. 6.c).
On their very own, these EOFs are difficult to interpret in bodily phrases. What underlying options are they capturing? Are these embeddings bodily significant? One option to simplify the interpretation is by specializing in probably the most excessive values in every distribution, as these are most strongly related to every EOF. Whereas this guide clustering method leaves a lot of the distribution close to the origin ambiguous, it permits us to separate the information into distinct teams that may be analyzed extra carefully. By making use of a σ > 2 threshold (represented by the skinny white dashed strains in Fig. 6.a-c), we will divide this 3D distribution of factors into six distinct teams of equal sampling quantity. Since visualizing this separation in 2D is especially difficult, we’ve offered an interactive information viewer (Fig. 8), created with Plotly, to make this distinction clearer. Be happy to click on on the determine beneath to discover the information your self.
With probably the most excessive EOF clusters chosen, we will now plot these in bodily variable areas to start deciphering them. That is demonstrated in Fig. 9 throughout completely different variable areas: n0-λ (panel a), Fs-Rho (panel b), λ-Dm (panel c), and Sr-Dm (panel d). Beginning with the purple and blue clusters in Fig. 9.a (representing the optimistic and damaging EOF1 values), we see a transparent separation in n0-λ house. The purple cluster, characterised by a excessive PSD intercept and slope, signifies a high-intensity grouping, suggestive of many small particles, whereas the blue cluster exhibits the other conduct. That is indicative of a possible depth embedding.
In panel b, there’s a definite separation between the purple and light-weight blue clusters (akin to the optimistic and damaging EOF2 values). The purple cluster, related to excessive fall velocity and density, contrasts with the sunshine blue cluster, which exhibits the other traits. This sample probably represents a particle temperature/wetness embedding, describing the “stickiness” of the snow because it falls. Hotter, denser particles (equivalent to partially melted or frozen particles) are inclined to fall quicker, very like how a slushy pellet falls quicker than a dry snowflake.
Lastly, in panels c and d, the yellow and magenta clusters are separated based mostly on PSD slope and mass-weighted imply diameter. Whereas much less clear, this implies a possible relationship with particle dimension and the underlying snowfall regime, equivalent to variations between advanced shallow programs and deep programs.
One other option to strengthen our confidence in these attributions is by evaluating the teams to unbiased observations. We will do that by cross-referencing the PCA-based snowfall classifications from the PIP with close by floor radar observations (i.e., a Micro Rain Radar) and reanalysis (i.e., ERA5) estimates to guage bodily consistency. That is one motive we advocate not at all times utilizing all accessible information within the dimensionality discount, because it limits the flexibility to later assess the robustness of the embeddings. To validate our method, we examined a sequence of case research at Marquette (MQT), Michigan, to see how effectively these classifications align. As an illustration, in Fig. 10, we observe a transition from a high-intensity snowstorm (purple) to partially melted mixed-phase snow crystals (sleet) as temperatures briefly rise above zero levels C (panel h), after which again to high-intensity snow as temperatures drop beneath zero later within the day. This additionally aligns with the modifications we see in reflectivity (panel a) and we will see this transition within the n0-λ plot in panel i.
Constructing on our PCA evaluation and the consistency noticed with collocated observations, we additionally created Fig. 11, which summarizes how the first linear embeddings recognized via PCA are distributed throughout completely different bodily variable areas. These classifications supply essential microphysical insights that may improve a priori datasets, finally bettering the accuracy of state-of-the-art fashions and snowfall retrievals.
Nonetheless, since PCA is proscribed to linear embeddings, this raises an vital query: are there nonlinear patterns inside this dataset that now we have but to discover? Moreover, what new insights may emerge if we lengthen this evaluation past snow to incorporate different forms of precipitation?
Let’s sort out these questions within the subsequent part!
3. Nonlinear dimensionality discount utilizing UMAP
https://doi.org/10.1126/sciadv.adu0162
With a view to study extra advanced, nonlinear embeddings, we have to contemplate a unique kind of unsupervised studying that loosens the linearity assumptions of methods like PCA. This brings us to the idea of manifold studying. The concept behind manifold studying is that high-dimensional information usually lie on a lower-dimensional, curved manifold throughout the authentic information house (McInnes et al., 2020). By mapping this manifold, we will uncover the underlying construction and relationships that linear strategies may miss. Methods like t-SNE, UMAP, VAEs, or Isomap can reveal these intricate patterns, offering a extra nuanced understanding of the dataset’s latent options. Making use of manifold studying to our dataset might uncover nonlinear embeddings that additional distinguish precipitation sorts, doubtlessly providing even deeper insights into the microphysical processes at play. As slightly trace as to what’s to return, see Fig. 12. As talked about earlier than, I received’t go into the implementation particulars of such strategies, as this has been lined many occasions right here on TDS.
Moreover, we want to use our whole dataset of each disdrometer observations and collocated floor metoeologic variables this time round to see if the extra dimensions present helpful context for higher differentiating between extremely advanced bodily processes. For instance, can we detect various kinds of mixed-phase precipitation if we knew extra in regards to the temperature and humidity on the time of remark? So, in contrast to the earlier part the place we restricted the inputs to simply PIP information and simply snowfall, we now embody all 12 dimensions for the complete dataset. This additionally considerably reduces our complete pattern right down to 128,233 5-minute durations at 7 areas, since not all websites have working floor meteorologic stations to drag information from. As is at all times the case with all these issues, as we add extra dimensions, we run up towards the dreaded curse of dimentionality.
Because the dimensionality of the characteristic house will increase, the variety of configurations can develop exponentially, and thus the variety of configurations lined by an remark decreases — Richard Bellman
This tradeoff within the variety of inputs and have sparsity is a problem we could have to bear in mind transferring ahead. Fortunately for us, we solely have 12 dimensions which can appear to be so much, however is de facto fairly small in comparison with many different tasks within the Pure Sciences with doubtlessly 1000’s of dimensions (Auton et al., 2015).
As talked about earlier, we explored a wide range of nonlinear fashions for this part of the undertaking (see Desk 2). In any Machine Studying (ML) undertaking we undertake, we desire to start out with less complicated, extra interpretable strategies and regularly progress to extra refined methods, as much less advanced approaches are sometimes extra environment friendly and simply understood.
With this technique in thoughts, we started by constructing on the outcomes from Half 2, utilizing PCA as soon as once more as a baseline for this bigger dataset of rain and snow particles. We then in contrast PCA to nonlinear methods equivalent to Isomap, VAEs, t-SNE, and UMAP. After conducting a sequence of sensitivity analyses, we discovered that UMAP outperformed the others in producing clear embeddings in a extra computationally environment friendly method, making it the main target of our dialogue right here. Moreover, with UMAP’s improved international separation of information throughout the manifold, we will transfer past guide clustering, using a extra goal technique like Hierarchical Density-Based mostly Spatial Clustering of Purposes with Noise (HDBSCAN) to group comparable circumstances collectively (McInnes et al., 2017).
Making use of UMAP to this 12-dimensional dataset resulted within the identification of three main latent embeddings (LEs). We experimented with numerous hyperparameters, together with the variety of embeddings, and located that, much like PCA, the primary two embeddings have been probably the most vital. The third embedding additionally displayed some separation between sure teams, however past this third stage, extra embeddings offered little separation and have been subsequently excluded from the evaluation (though these may be attention-grabbing to take a look at extra in future work). The primary two LEs, together with a case examine instance from Marquette, Michigan, illustrating discrete information factors over a 24-hour interval, are proven beneath in Fig. 13.
Instantly, we discover a number of key variations from the earlier snowfall-focused examine utilizing PCA. With the addition of rain and mixed-phase information, the primary and second empirical orthogonal capabilities (EOF1 and EOF2) have now swapped locations. The first embedding now encodes details about particle part quite than depth. Depth shifts to the second latent embedding (LE2), remaining vital however now secondary. The third LE nonetheless seems to narrate to particle dimension and form, notably throughout the snowfall portion of the manifold.
Making use of HDBSCAN to the manifold teams generated by UMAP resulted in 9 distinct clusters, plus one ambiguous cluster (Fig. 13.a). The separation between clusters is way clearer in comparison with PCA, and these teams appear to signify distinct bodily precipitation processes, starting from snowfall to mixed-phase to rainfall at numerous depth ranges. Curiously, the ambiguous factors and the connections between nodes within the graph kind distinct pathways of particle behavior evolution. This discovering is especially intriguing because it outlines clear particle evolutionary pathways, exhibiting how a raindrop can remodel right into a frozen snow crystal beneath the correct atmospheric situations.
An actual-world instance of this phenomenon is proven in Fig. 13.b, noticed in Marquette on February 15, 2023. Every coloured ring represents a person (5-minute) information level all through the day, with an arrow indicating the route of time. In Fig. 13.c, we overlay ancillary radar observations with floor temperatures. Up till round 12:00 UTC, a transparent brightband in reflectivity could be seen at roughly 1 km, indicative of a melting layer the place temperatures are heat sufficient for snow to soften into rain. This era was appropriately labeled as rainfall utilizing our UMAP+HDBSCAN (UH) clustering technique. Then, round 17:00 UTC, temperatures quickly dropped effectively beneath freezing, resulting in the classification of particles as mixed-phase and ultimately as snowfall. A lot of these checks are critically vital for ensuring what your manifold form suggests is smart bodily.
When you’d prefer to discover this manifold your self, inspecting completely different websites and seeing how numerous variables map to the embedding, try our interactive information evaluation instrument, or click on Fig. 14 beneath.
If you discover the instrument talked about above, you’ll discover that mapping numerous enter options to the manifold embedding ends in easy gradients. These gradients point out that the overall international construction of the information is probably going being captured in a significant means, providing beneficial insights into what the embeddings are encoding.
Evaluating the separation of factors utilizing UMAP to that of PCA (the place PCA is utilized to the very same dataset as UMAP) reveals considerably higher separation with UMAP, particularly regarding precipitation part. Whereas PCA can broadly distinguish between “liquid” and “strong” particles, it struggles with the extra advanced mixed-phase particles. This limitation is obvious within the distributions proven in Fig. 15.d-e. PCA usually suffers from variance overcrowding close to the origin, resulting in a tradeoff between the variety of clusters we will establish and the dimensions of the ambiguous supercluster. Though HDBSCAN could be utilized to PCA in the identical method as UMAP, it solely generates two clusters (rain and snow) which isn’t notably helpful by itself, and could be achieved with a easy linear threshold. In distinction, UMAP gives a lot better separation, leading to 37% fewer ambiguous factors and a +0.14 larger silhouette rating for the clusters in comparison with PCA (0.51).
As we did beforehand with PCA, we will conduct a sequence of case examine comparisons when utilizing UMAP to strengthen our bodily cluster attributions. By evaluating these with collocated MRR observations, we will assess whether or not the situations reported within the astmosphere above the PIP align with the attributions produced by the UH clusters, and the way these evaluate to the clusters from PCA. In Fig. 16 beneath, we study a number of of those circumstances at Marquette.
Within the first column (a), we current an instance of a chronic mixed-phase occasion, emphasizing LE1, which we all know occurred at MQT from recorded climate reviews. Alongside the highest panel, each PCA and UMAP establish the interval up till 19:00 UTC as rain. Nonetheless, after this era, the PCA groupings turn into sparse and largely ambiguous, whereas UMAP efficiently maps the post-19:00 UTC interval as mixed-phase, distinguishing between moist sleet (inexperienced) and colder, slushy pellets (purple).
In panel (b), we spotlight a case specializing in depth modifications (LE2), the place situations shift from high-intensity mixed-phase to low-intensity mixed-phase, after which again to high-intensity snowfall as temperatures cool. Once more, UMAP gives a extra detailed and constant classification in comparison with the sparser outcomes from PCA.
Lastly, in panel (c), we discover an LE3 case involving a shallow system till 15:00 UTC, adopted by a deep convective system transferring over the location, resulting in a rise within the dimension, form complexity, and depth of the snow particles. Right here too, UMAP demonstrates a extra complete mapping of the occasion. Observe that these are only some handpicked case research nevertheless, and we advocate testing our full paper for multi-year comparisons.
Total, we discovered that the nonlinear 3D manifold generated utilizing UMAP offered a easy and correct approximation of precipitation part, depth, and particle dimension/form (Fig. 17). When mixed with hierarchical density-based clustering, the ensuing teams have been distinct and bodily in keeping with unbiased observations. Whereas PCA was capable of seize the overall embedding construction (with EOFs 1-3 largely analogous to LEs 1-3), it struggled to signify the worldwide construction of the information, as many of those processes are inherently nonlinear.
So what does this all imply?
Conclusions
You’ve made it to the top!
I understand this has been a prolonged submit, so I’ll hold this part temporary. In abstract, we’ve developed a high-quality dataset of precipitation observations from a number of websites over a number of years and used this information to use each linear and nonlinear dimensionality discount methods, aiming to be taught extra in regards to the construction of the information itself! Throughout all strategies, embeddings associated to particle part, precipitation depth, and particle dimension/form have been probably the most dominant. Nonetheless, solely the nonlinear methods have been capable of seize the advanced international construction of the information, revealing distinct precipitation teams that aligned effectively with unbiased observations.
We consider these teams (and particle transitionary pathways) can be utilized to enhance present satellite tv for pc precipitation retrievals in addition to numerical mannequin microphysical parameterizations. With this in thoughts, now we have constructed an operational parameter matrix (the lookup house is illustrated in Fig. 18) which produces a easy conditional chance vector for every group based mostly on temperature (T) and particle counts (Nt). Please see the related manuscript for entry/API particulars to this desk.
Nonlinear dimensionality discount methods like UMAP are nonetheless comparatively new and have but to be extensively utilized to the big datasets rising within the Geosciences. It must be famous that these methods are imperfect, and there are tradeoffs based mostly in your drawback context, so hold that in thoughts. Nonetheless, our findings right here, constructing first on PCA, counsel that these methods could be extremely efficient, emphasizing the worth of fastidiously curated and complete observational databases, which we hope to see extra of within the coming years.
Thanks once more for studying, and tell us within the feedback how you might be desirous about studying extra out of your giant observational datasets!
Information and Code
PIP and floor meteorologic observations used as enter to the PCA and UMAP are publicly accessible for obtain on the College of Michigan’s DeepBlue information repository (https://doi.org/10.7302/37yx-9q53). This dataset is offered as a sequence of folders containing NetCDF information for every website and 12 months, with standardized CF metadata naming conventions. For extra detailed info, please see our information paper (https://doi.org/10.1029/2024EA003538). ERA5 information could be downloaded from the Copernicus Local weather Information Retailer.
PIP information preprocessing code is on the market on our public GitHub repository (https://github.com/frasertheking/pip_processing), and now we have offered a customized API for interacting with the particle microphysics information in Python referred to as pipdb (https://github.com/frasertheking/pipdb). The snowfall PCA undertaking code is on the market on Github (https://github.com/frasertheking/snowfall_pca). Moreover, the code used to suit the DR strategies, cluster circumstances, analyze inputs and generate figures can also be accessible for obtain on a separate, public GitHub repository (https://github.com/frasertheking/umap).
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