When Does Advection-Aware Graph Nowcasting Help? A Controlled Study of Distributed Solar Ramp Forecasting with a Self-Supervised Cloud-Motion Estimator

# When Does Advection-Aware Graph Nowcasting Help?A Controlled Study of Distributed Solar Ramp Forecastingwith a Self-Supervised Cloud-Motion Estimator
Source: [https://arxiv.org/html/2609.30286](https://arxiv.org/html/2609.30286)
September 8, 2026

###### Abstract

Short\-term forecasting of cloud\-induced power ramps across a network of distributed photovoltaic \(PV\) or irradiance sensors is a recognised pain point for grid operators\. A natural idea is to make the graph neural network \(GNN\)*advection\-aware*: connect each site to the sites upwind of it, with edge time\-lags set by the cloud\-motion vector \(CMV\), so that a ramp is propagated forward before it physically arrives\. Using a controlled synthetic testbed with a known wind field, we show that \(i\) with a realistic cross\-correlation CMV estimate, an explicit advection graph does*not*beat a plain static or learned\-adjacency spatiotemporal GNN; \(ii\) roughly half of the benefit available from a perfect CMV comes simply from providing an accurate motion vector as an input feature, not from graph structure; and \(iii\) advection helps only when the advective displacement over the forecast horizon,v⋅Hv\\cdot H, fits inside the sensor network\. Motivated by \(ii\), we introduce a small*self\-supervised*cloud\-motion estimator—a position\-aware encoder trained only on a multi\-lag optical\-flow reconstruction objective with an annealed kernel—that recovers the true wind vector to2°2\\text\{\\,\}\\mathrm\{\\SIUnitSymbolDegree\}–4°4\\text\{\\,\}\\mathrm\{\\SIUnitSymbolDegree\}median angular error,22–4×4\\timesbetter than the classical cross\-correlation method across every wind regime\. Freezing this estimator and feeding its vector to the forecaster closes about60%60\\text\{\\,\}\\mathrm\{\\%\}of the oracle\-CMV RMSE gap at moderate wind \(8%to15%8\\text\{\\,\}\\mathrm\{\\%\}15\\text\{\\,\}\\mathrm\{\\%\}RMSE reduction over no advection\), with no external wind data\. We also report a negative result for a spatially\-coherent probabilistic head\. All claims are established on a single synthetic simulator; we discuss why real\-network validation is the necessary next step and outline it\.

## 1Introduction

Integrating large amounts of solar generation exposes grid operators to*ramps*: sudden minutes\-scale drops or surges in aggregate PV output as cloud shadows sweep across a region\. Deterministic root\-mean\-square error \(RMSE\), the usual training and reporting metric, is dominated by smooth clear\-sky periods and hides exactly these events\. Spatiotemporal GNNs are a popular tool for distributed solar forecasting\[[16](https://arxiv.org/html/2609.30286#bib.bib16)\], but they almost universally use a*static, symmetric*graph, which ignores that cloud information has a direction and a travel time set by the wind\.

This paper asks a simple question:*does making the graph advection\-aware actually help, and if so, when?*We build a controlled synthetic testbed in which clouds are a Gaussian random field advected by a known, slowly varying wind, so that a ground\-truth CMV is available for every forecast origin\. Against this oracle we can cleanly separate three things that are usually entangled: the benefit of the advection*graph*, the benefit of an accurate motion*feature*, and the cost of*estimating*the motion from data\.

#### Contributions\.

1. 1\.A controlled decomposition of the advection\-aware nowcasting problem \(Sec\.[5\.1](https://arxiv.org/html/2609.30286#S5.SS1)–[5\.2](https://arxiv.org/html/2609.30286#S5.SS2)\): with a realistic CMV estimate the advection graph does not beat plain baselines; roughly half the oracle\-CMV benefit is an accurate*input feature*, not graph structure; and the benefit exists only inside av⋅H≲v\\cdot H\\lesssimnetwork\-extent envelope\.
2. 2\.A smallself\-supervised cloud\-motion estimator\(Sec\.[5\.3](https://arxiv.org/html/2609.30286#S5.SS3)\) that recovers the true wind to2°to4°2\\text\{\\,\}\\mathrm\{\\SIUnitSymbolDegree\}4\\text\{\\,\}\\mathrm\{\\SIUnitSymbolDegree\}median angular error—22–4×4\\timesbetter than the classical cross\-correlation method—using only a multi\-lag optical\-flow reconstruction loss with an annealed kernel and a position\-aware encoder\.
3. 3\.Afrozen two\-stage forecaster\(Sec\.[5\.4](https://arxiv.org/html/2609.30286#S5.SS4)\) that uses this estimator and closes∼\\sim60%60\\text\{\\,\}\\mathrm\{\\%\}of the oracle\-CMV RMSE gap at moderate wind, with a clean operating envelope\.
4. 4\.Negative results, reported plainly: the advection graph alone \(Sec\.[5\.1](https://arxiv.org/html/2609.30286#S5.SS1)\), coupling the motion estimate to the forecast loss \(Sec\.[5\.3](https://arxiv.org/html/2609.30286#S5.SS3)\), and a spatially\-coherent probabilistic head \(Sec\.[5\.5](https://arxiv.org/html/2609.30286#S5.SS5)\)\.

#### Scope\.

Every result here is on one synthetic simulator\. The synthetic “true wind” is a generative parameter, so the CMV\-recovery result in particular must be read as a controlled sanity check, not a claim about real skies\. We are explicit about this in Sec\.[6](https://arxiv.org/html/2609.30286#S6.SS0.SSS0.Px3)and describe the real\-data study it calls for\.

## 2Related work

#### Spatiotemporal GNN forecasting\.

Modelling a set of geographically distributed series as signals on a graph and applying graph\-convolutional or graph\-attention layers with a temporal encoder is now standard in traffic forecasting—DCRNN\[[9](https://arxiv.org/html/2609.30286#bib.bib9)\], STGCN\[[20](https://arxiv.org/html/2609.30286#bib.bib20)\], Graph WaveNet\[[18](https://arxiv.org/html/2609.30286#bib.bib18)\], ASTGCN\[[5](https://arxiv.org/html/2609.30286#bib.bib5)\]—and has been carried over to multi\-site PV power forecasting, e\.g\. the graph\-convolutional LSTM/transformer models of[Simeunović et al\. \[16\]](https://arxiv.org/html/2609.30286#bib.bib16)\. The adjacency is almost always*static*, built from geographic distance or historical correlation; Graph WaveNet additionally learns a global adjacency, which we include as a baseline\. None of these encode cloud advection explicitly\.

#### Solar nowcasting and cloud motion\.

Minutes\-ahead irradiance forecasting has a long history using sky imagers\[[2](https://arxiv.org/html/2609.30286#bib.bib2)\], satellite imagery, and cloud tracking; see[Yang et al\. \[19\]](https://arxiv.org/html/2609.30286#bib.bib19)for a review\. The dominant non\-image approach on a sparse ground network is to estimate a rigid cloud\-motion vector \(CMV\) by cross\-correlating pairs of clear\-sky\-index series and solving a least\-squares problem for the translation velocity\[[1](https://arxiv.org/html/2609.30286#bib.bib1),[10](https://arxiv.org/html/2609.30286#bib.bib10)\], then “advect the observed field forward”\[[12](https://arxiv.org/html/2609.30286#bib.bib12)\]\. Our synthetic\-field advection feature is the GNN analogue of that heuristic, and our self\-supervised estimator is an optical\-flow\-style\[[7](https://arxiv.org/html/2609.30286#bib.bib7)\]objective specialised to a sparse sensor layout\.

#### Learned advection in weather nowcasting\.

Precipitation nowcasting has moved from ConvLSTM\[[15](https://arxiv.org/html/2609.30286#bib.bib15)\]to large advection\-aware neural models such as MetNet\[[17](https://arxiv.org/html/2609.30286#bib.bib17)\]and DGMR\[[13](https://arxiv.org/html/2609.30286#bib.bib13)\], which learn motion implicitly from dense radar rasters\. Distributed solar sensing gives only a sparse, irregular sample of the field, which is the regime we study\.

#### Ramp forecasting and probabilistic scores\.

Ramp events lack a single definition; the swinging\-door construction of[Florita et al\. \[3\]](https://arxiv.org/html/2609.30286#bib.bib3)is a common choice, which we adopt for our ramp\-capture metrics\. For the probabilistic head we use strictly proper multivariate scores—the energy score\[[4](https://arxiv.org/html/2609.30286#bib.bib4)\]and the variogram score\[[14](https://arxiv.org/html/2609.30286#bib.bib14)\]\. Clear\-sky index uses the Haurwitz model\[[6](https://arxiv.org/html/2609.30286#bib.bib6)\]; the Ineichen–Perez model\[[8](https://arxiv.org/html/2609.30286#bib.bib8)\]is a common alternative\.

## 3Problem setup and synthetic testbed

We forecast the clear\-sky indexkt=GHI/GHIcsk\_\{t\}=\\mathrm\{GHI\}/\\mathrm\{GHI\}\_\{\\mathrm\{cs\}\}atNNfixed sites,HHsteps ahead \(H=16H=16at30s30\\text\{\\,\}\\mathrm\{s\}, i\.e\. 8 minutes\)\. Clouds are a periodic Gaussian random field of optical depth, translated by a wind vector𝐯⁡\(t\)\\mathbf\{v\}\(t\)that performs a bounded random walk \(a*steadiness*knob controls its variance\); an*evolving*option blends keyframe fields so the pattern also grows and decays\. Observed GHI is clear\-sky GHI\[[6](https://arxiv.org/html/2609.30286#bib.bib6)\]times a transmittance function of the local optical depth, plus noise\. The simulator emits, per origin, the site series, the true𝐯⁡\(t\)\\mathbf\{v\}\(t\)\(the*oracle*CMV\), and a classical cross\-correlation estimate𝐯est\\mathbf\{v\}\_\{\\mathrm\{est\}\}\[[1](https://arxiv.org/html/2609.30286#bib.bib1)\]\. Default layout:N=49N=49on a1km1\\text\{\\,\}\\mathrm\{k\}\\mathrm\{m\}grid \(∼\\sim7km7\\text\{\\,\}\\mathrm\{k\}\\mathrm\{m\}across\)\. We report test RMSE onktk\_\{t\}and ramp\-capture metrics; means are over 2–3 seeds\.

## 4Methods

#### Advection\-aware graph\.

Given a motion vector𝐯\\mathbf\{v\}, for each sitejjand horizonhhthe arriving cloud is currently near𝐩j−𝐯​h​Δ​t\\mathbf\{p\}\_\{j\}\-\\mathbf\{v\}\\,h\\,\\Delta t\. We connectj​@​hj@hto itskknearest sensors there with distance\-weighted, per\-\(j,h\)\(j,h\)\-normalised weightsw∝exp\(−d2/ℓ2\)w\\propto\\exp\(\-d^\{2\}/\\ell^\{2\}\),ℓ\\ellthe median nearest\-neighbour spacing, and pool their embeddings into an\(N,H,d\)\(N,H,d\)feature for the forecast head—the GNN form of “advect the field forward”\[[12](https://arxiv.org/html/2609.30286#bib.bib12)\]\. An off\-grid reliability gate down\-weights\(j,h\)\(j,h\)whose upwind point lands far from any sensor\.

#### Forecaster\.

A per\-site GRU temporal encoder feedsLLheterogeneous message\-passing layers overkk\-NN and historical\-correlation edge types, each with its own message MLP and a gated residual update; the advection feature enters at the head through a gated correction\. Baselines: smart persistence, per\-site GRU, static\-distance GCN, and a learned\-adjacency GNN \(a Graph WaveNet\-style global adjacency\[[18](https://arxiv.org/html/2609.30286#bib.bib18)\]\)\. Ramp events use the swinging\-door construction\[[3](https://arxiv.org/html/2609.30286#bib.bib3)\]\.

#### Self\-supervised cloud\-motion estimator\.

A rigidly advecting field obeyskt​\(𝐱,t\)=kt​\(𝐱−𝐯​L​Δ​t,t−L\)k\_\{t\}\(\\mathbf\{x\},t\)=k\_\{t\}\(\\mathbf\{x\}\-\\mathbf\{v\}L\\Delta t,\\,t\-L\)\. We train a small position\-aware encoder \(per\-site GRU\+\+a geometry\-preserving DeepSets pool\) to output𝐯^\\hat\{\\mathbf\{v\}\}, minimising the residual of this identity, interpolated from the sensor field, summed over several lagsL∈\{2,4,6,8,10\}L\\in\\\{2,4,6,8,10\\\}\(one𝐯^\\hat\{\\mathbf\{v\}\}must explain them all\):

ℒrec\(𝐯^\)=1\|ℒ\|∑L∥kt\(⋅,t\)−∑isoftmaxi\(−∥𝐩⋅−𝐯^LΔt−𝐩i∥2/τ2\)kt\(𝐩i,t−L\)∥2\.\\mathcal\{L\}\_\{\\mathrm\{rec\}\}\(\\hat\{\\mathbf\{v\}\}\)\\;=\\;\\frac\{1\}\{\|\\mathcal\{L\}\|\}\\sum\_\{L\}\\Big\\\|\\,k\_\{t\}\(\\cdot,t\)\-\\textstyle\\sum\_\{i\}\\mathrm\{softmax\}\_\{i\}\\\!\\big\(\-\\\|\\mathbf\{p\}\_\{\\cdot\}\-\\hat\{\\mathbf\{v\}\}L\\Delta t\-\\mathbf\{p\}\_\{i\}\\\|^\{2\}/\\tau^\{2\}\\big\)\\,k\_\{t\}\(\\mathbf\{p\}\_\{i\},t\-L\)\\,\\Big\\\|^\{2\}\.\(1\)The softmax widthτ\\tauis annealed from0\.400\.40to0\.100\.10of the network diameter \(largeτ\\taugives useful gradients far from the optimum; smallτ\\tausharpens the estimate\)\. An optional light MSE\-to\-reference term stands in for a small amount of numerical\-weather\-prediction \(NWP\) wind on real data\.

#### Two\-stage forecaster\.

We*pre\-train*the estimator,*freeze*it, and feed𝐯^\\hat\{\\mathbf\{v\}\}into \(a\) the encoder’s motion input channels and \(b\) the advection graph\. Freezing avoids a failure mode we observed when𝐯^\\hat\{\\mathbf\{v\}\}is trained jointly with the forecast loss: the loss drives𝐯^→𝟎\\hat\{\\mathbf\{v\}\}\\to\\mathbf\{0\}\(Sec\.[5\.3](https://arxiv.org/html/2609.30286#S5.SS3)\)\.

## 5Experiments

### 5\.1Does an advection graph help? \(E1\)

With the classical CMV estimate, we sweep wind speed and compare the forecaster with and without the advection feature against baselines \(Fig\.[1](https://arxiv.org/html/2609.30286#S5.F1), Table[1](https://arxiv.org/html/2609.30286#S5.T1)\)\. The heterogeneous GNN*without*advection is the best or tied\-best model at low–moderate wind; a learned global adjacency wins at high wind and under non\-stationary/evolving clouds\. Adding the advection feature on top of the estimated CMV never helps and costs up to10%10\\text\{\\,\}\\mathrm\{\\%\}RMSE at10m/s10\\text\{\\,\}\\mathrm\{m\}\\mathrm\{/\}\\mathrm\{s\}\. On a dense grid every upwind sensor is already a graph neighbour, so learned spatial mixing captures advection implicitly\.

Figure 1:E1\.Test RMSE vs\. wind speed, estimated CMV, 2 seeds \(±\\pms\.d\.\)\. The advection feature \(top line\) does not beat the heterogeneous GNN without it, nor the learned\-adjacency baseline\.Table 1:E1test RMSE \(clear\-sky index\), estimated CMV, 2 seeds\. Lower is better; best per column inbold\.
### 5\.2The cloud\-motion bottleneck \(E2 and decomposition\)

Replacing the estimated CMV with the*oracle*flips the picture: with a perfect wind vector the advection feature cuts RMSE by14%to17%14\\text\{\\,\}\\mathrm\{\\%\}17\\text\{\\,\}\\mathrm\{\\%\}and lifts ramp\-down capture \(CSI\) by about 5 points \(Table[2](https://arxiv.org/html/2609.30286#S5.T2)\)\. A finer decomposition at10m/s10\\text\{\\,\}\\mathrm\{m\}\\mathrm\{/\}\\mathrm\{s\}\(2 seeds\) shows*where*that benefit lives: no advection0\.0870\.087; true wind in the graph only0\.0820\.082; true wind in the graph*and*as an input feature0\.0660\.066; oracle skyline0\.0640\.064\. Roughly half of the oracle\-CMV advantage is simply an accurate motion vector broadcast as an input feature; the rest is graph structure\.

Table 2:E2\.Advection feature value depends on CMV quality \(test RMSE, 2 seeds\)\.
### 5\.3Self\-supervised cloud\-motion estimation

Trained standalone onℒrec\\mathcal\{L\}\_\{\\mathrm\{rec\}\}, the estimator’s median angular error is2°to4°2\\text\{\\,\}\\mathrm\{\\SIUnitSymbolDegree\}4\\text\{\\,\}\\mathrm\{\\SIUnitSymbolDegree\}in steady wind and7°to13°7\\text\{\\,\}\\mathrm\{\\SIUnitSymbolDegree\}13\\text\{\\,\}\\mathrm\{\\SIUnitSymbolDegree\}in variable wind—22–4×4\\timesbetter than the classical cross\-correlation estimate \(14°to31°14\\text\{\\,\}\\mathrm\{\\SIUnitSymbolDegree\}31\\text\{\\,\}\\mathrm\{\\SIUnitSymbolDegree\}\) in every regime \(Fig\.[2](https://arxiv.org/html/2609.30286#S5.F2), Table[3](https://arxiv.org/html/2609.30286#S5.T3)\)\. A light supervision term \(weight0\.10\.1\) tightens the hard cases to2°to8°2\\text\{\\,\}\\mathrm\{\\SIUnitSymbolDegree\}8\\text\{\\,\}\\mathrm\{\\SIUnitSymbolDegree\}; it is not required\. Ablation: the position\-aware encoder is what matters; kernel annealing and the classical\-estimate prior are minor\.

*Negative result\.*An earlier design that reused the forecaster’s embeddings and trained𝐯^\\hat\{\\mathbf\{v\}\}jointly with the forecast loss was unstable \(recovered cosine swung0\.30\.3–0\.990\.99across module and loss variants\); feeding𝐯^\\hat\{\\mathbf\{v\}\}to the head while coupled to the forecast loss collapses it to𝐯^→𝟎\\hat\{\\mathbf\{v\}\}\\to\\mathbf\{0\}\. Decoupling \(standalone encoder, frozen after pre\-training\) removes this\.

Figure 2:Self\-supervised cloud\-motion estimation\.Median angular error of𝐯^\\hat\{\\mathbf\{v\}\}vs\. the true wind, 3 seeds\. The learned estimator beats the classical cross\-correlation method in every wind regime\.Table 3:CMV estimatormedian angular error \(deg\), 3 seeds\.
### 5\.4Frozen two\-stage forecaster

Pre\-training the estimator, freezing it, and feeding𝐯^\\hat\{\\mathbf\{v\}\}to the forecaster closes about60%60\\text\{\\,\}\\mathrm\{\\%\}of the oracle\-CMV RMSE gap at moderate wind \(8%to15%8\\text\{\\,\}\\mathrm\{\\%\}15\\text\{\\,\}\\mathrm\{\\%\}RMSE reduction over no advection\), tight across 3 seeds \(Fig\.[3](https://arxiv.org/html/2609.30286#S5.F3), Table[4](https://arxiv.org/html/2609.30286#S5.T4)\)\. At≥\\geq16m/s16\\text\{\\,\}\\mathrm\{m\}\\mathrm\{/\}\\mathrm\{s\}advection does not help*even with the oracle*: the advective displacement over the horizon \(7\.7kmto9\.6km7\.7\\text\{\\,\}\\mathrm\{k\}\\mathrm\{m\}9\.6\\text\{\\,\}\\mathrm\{k\}\\mathrm\{m\}\) exceeds the∼\\sim7km7\\text\{\\,\}\\mathrm\{k\}\\mathrm\{m\}network, so there is no on\-grid upwind information\. The off\-grid gate prevents a catastrophic regression but cannot manufacture signal\.Operating envelope: advection nowcasting helps iffv⋅Hv\\cdot Hfits within the network\.

Figure 3:Frozen two\-stage forecaster, 3 seeds \(±\\pms\.d\.\)\. Green labels: fraction of the no\-advection→\\tooracle gap closed\. In the shaded region \(v⋅Hv\\cdot Hoff\-grid\) even the oracle does not beat no advection\.Table 4:Frozen two\-stagetest RMSE \(clear\-sky index\), 3 seeds\.
### 5\.5Spatially\-coherent probabilistic head \(negative\)

We tried a joint low\-rank\-plus\-diagonal Gaussian head across sites \(for fleet\-aggregate ramp risk\), trained by exact Woodbury NLL, versus a diagonal head\. It was marginally*worse*on every metric, including the energy\[[4](https://arxiv.org/html/2609.30286#bib.bib4)\]and variogram\[[14](https://arxiv.org/html/2609.30286#bib.bib14)\]scores it is meant to improve \(e\.g\. at16m/s16\\text\{\\,\}\\mathrm\{m\}\\mathrm\{/\}\\mathrm\{s\}: variogram52\.652\.6vs\.51\.051\.0; CRPS0\.0650\.065vs\.0\.0630\.063\)\. After conditioning on the graph features the site residuals appear to carry little extra dependence; we report this as a negative result pending a dedicated study\.

## 6Discussion

#### When to use what\.

The results give a concrete rule\. Ifv⋅Hv\\cdot Hfits inside the sensor network and the wind is reasonably steady, an advection\-aware feature driven by a good CMV estimate is worth8%to15%8\\text\{\\,\}\\mathrm\{\\%\}15\\text\{\\,\}\\mathrm\{\\%\}RMSE\. Otherwise—fast wind, very sparse or irregular networks, strongly non\-stationary clouds—a learned global adjacency is the better tool, and the advection feature is at best neutral \(with the gate\) and at worst a10%10\\text\{\\,\}\\mathrm\{\\%\}regression \(without it\)\.

#### The estimator is the reusable piece\.

Independent of the forecasting question, the self\-supervised CMV estimator is a drop\-in replacement for cross\-correlation on any bare sensor network, several times more accurate here, and it needs no labels\.

#### Limitations\.

All experiments use one synthetic simulator, and its “true wind” is a generative parameter—so the CMV\-recovery numbers are a controlled sanity check, not a measurement on real skies, and the oracle gap that Sec\.[5\.4](https://arxiv.org/html/2609.30286#S5.SS4)closes is defined by that simulator\. Real clouds have multiple layers, shear, growth and decay, and no single motion vector\. The necessary next step is validation on a real distributed network—e\.g\. the NREL Oahu Solar Measurement Grid\[[11](https://arxiv.org/html/2609.30286#bib.bib11)\]\(17 sensors,1km1\\text\{\\,\}\\mathrm\{k\}\\mathrm\{m\},1Hz1\\text\{\\,\}\\mathrm\{H\}\\mathrm\{z\}\) for the forecaster, and a sky\-image dataset with optical\-flow motion for the estimator\. Our released code includes loaders and configs for these; only the raw data acquisition remains\.

## 7Conclusion

On a controlled testbed, an advection\-aware graph feature for distributed solar ramp nowcasting helps only within av⋅H≲network\-extentv\\cdot H\\lesssim\\text\{network\-extent\}envelope, and about half of its value is an accurate motion*feature*rather than graph structure\. A small self\-supervised estimator supplies that motion several times more accurately than the classical method, and a frozen two\-stage forecaster built on it closes∼\\sim60%60\\text\{\\,\}\\mathrm\{\\%\}of the oracle\-CMV gap at moderate wind\. We release the simulator, models, metrics, and experiment scripts\.

#### Reproducibility\.

The simulator, models, metrics, baselines, and experiment scripts are available at[https://github\.com/appsofa\-com/gnn\-solar\-energy](https://github.com/appsofa-com/gnn-solar-energy)\(branchsolar\-ramp\-nowcasting\); every table and figure is regenerated from committed result files\.pytestcovers the simulator, graph construction, metrics, and model shapes \(40 tests\)\.

## References

- \[1\]J\. L\. Bosch, Y\. Zheng, and J\. Kleissl\.Deriving cloud velocity from an array of solar radiation measurements\.*Solar Energy*, 87:196–203, 2013\.
- \[2\]C\. W\. Chow, B\. Urquhart, M\. Lave, A\. Dominguez, J\. Kleissl, J\. Shields, and B\. Washom\.Intra\-hour forecasting with a total sky imager at the UC San Diego solar energy testbed\.*Solar Energy*, 85\(11\):2881–2893, 2011\.
- \[3\]A\. Florita, B\.\-M\. Hodge, and K\. Orwig\.Identifying wind and solar ramping events\.In*IEEE Green Technologies Conference*, 2013\.
- \[4\]T\. Gneiting and A\. E\. Raftery\.Strictly proper scoring rules, prediction, and estimation\.*Journal of the American Statistical Association*, 102\(477\):359–378, 2007\.
- \[5\]S\. Guo, Y\. Lin, N\. Feng, C\. Song, and H\. Wan\.Attention based spatial\-temporal graph convolutional networks for traffic flow forecasting\.In*AAAI Conference on Artificial Intelligence*, 2019\.
- \[6\]B\. Haurwitz\.Insolation in relation to cloudiness and cloud density\.*Journal of Meteorology*, 2\(3\):154–166, 1945\.
- \[7\]B\. K\. P\. Horn and B\. G\. Schunck\.Determining optical flow\.*Artificial Intelligence*, 17\(1–3\):185–203, 1981\.
- \[8\]P\. Ineichen and R\. Perez\.A new airmass independent formulation for the Linke turbidity coefficient\.*Solar Energy*, 73\(3\):151–157, 2002\.
- \[9\]Y\. Li, R\. Yu, C\. Shahabi, and Y\. Liu\.Diffusion convolutional recurrent neural network: Data\-driven traffic forecasting\.In*International Conference on Learning Representations \(ICLR\)*, 2018\.
- \[10\]V\. P\. A\. Lonij, A\. E\. Brooks, A\. D\. Cronin, M\. Leuthold, and K\. Koch\.Intra\-hour forecasts of solar power production using measurements from a network of irradiance sensors\.*Solar Energy*, 97:58–66, 2013\.
- \[11\]National Renewable Energy Laboratory\.Oahu solar measurement grid \(1\-year archive\): 1\-second solar irradiance; Oahu, Hawaii\.NREL Data Catalog, DOI 10\.7799/1052451, 2010\.
- \[12\]L\. Nonnenmacher and C\. F\. M\. Coimbra\.Streamline\-based method for intra\-day solar forecasting through remote sensing\.*Solar Energy*, 108:447–459, 2014\.
- \[13\]S\. Ravuri, K\. Lenc, M\. Willson, D\. Kangin, R\. Lam, P\. Mirowski, et al\.Skilful precipitation nowcasting using deep generative models of radar\.*Nature*, 597:672–677, 2021\.
- \[14\]M\. Scheuerer and T\. M\. Hamill\.Variogram\-based proper scoring rules for probabilistic forecasts of multivariate quantities\.*Monthly Weather Review*, 143\(4\):1321–1334, 2015\.
- \[15\]X\. Shi, Z\. Chen, H\. Wang, D\.\-Y\. Yeung, W\.\-K\. Wong, and W\.\-C\. Woo\.Convolutional LSTM network: A machine learning approach for precipitation nowcasting\.In*Advances in Neural Information Processing Systems \(NeurIPS\)*, 2015\.
- \[16\]J\. Simeunović, B\. Schubnel, P\.\-J\. Alet, and R\. E\. Carrillo\.Spatio\-temporal graph neural networks for multi\-site PV power forecasting\.*IEEE Transactions on Sustainable Energy*, 13\(2\):1210–1220, 2022\.
- \[17\]C\. K\. Sønderby, L\. Espeholt, J\. Heek, M\. Dehghani, A\. Oliver, T\. Salimans, S\. Agrawal, J\. Hickey, and N\. Kalchbrenner\.MetNet: A neural weather model for precipitation forecasting\.*arXiv:2003\.12140*, 2020\.
- \[18\]Z\. Wu, S\. Pan, G\. Long, J\. Jiang, and C\. Zhang\.Graph WaveNet for deep spatial\-temporal graph modeling\.In*International Joint Conference on Artificial Intelligence \(IJCAI\)*, 2019\.
- \[19\]D\. Yang, J\. Kleissl, C\. A\. Gueymard, H\. T\. C\. Pedro, and C\. F\. M\. Coimbra\.History and trends in solar irradiance and PV power forecasting: A preliminary assessment and review using text mining\.*Solar Energy*, 168:60–101, 2018\.
- \[20\]B\. Yu, H\. Yin, and Z\. Zhu\.Spatio\-temporal graph convolutional networks: A deep learning framework for traffic forecasting\.In*International Joint Conference on Artificial Intelligence \(IJCAI\)*, 2018\.