deep learning powered rainfall prediction

Deep Learning Powered Rainfall Prediction

Presenter: Prof. Lei CHENDate: March 26, 2021

1 Background

2 Temporal Prediction

3 Spatial Estimation

4 Future Work

| CONTENTS

March 26, 2021Deep Learning Powered Rainfall Prediction 3

• Rainfall is one of the most basic meteorological and hydrological elements.

• Providing an accurate rainfall estimate, in both time and space, is an important task for natural disaster pre-warning.

1. Background

Floods

LandslidesRainfall Events


However, providing an accurate rainfall estimate is a non-trivial task.

1. Background

Tinyinitialerror

Hugeoutputerror

Rainfall: famous chaotic system

• Chaotic system• Extremely complex spatiotemporal variability and physical mechanism

• E.g., Convection → heavy rain, but “convection is not explicitly resolved”.

“Sub-daily precipitation extremes are often produced by

convective events, but conventional global and regional

climate models are not able to simulate such events well

because of limited spatial and temporal resolution and

because convection is not explicitly resolved”

Zhang X , Zwiers F W , Li G , et al. Complexity in estimating past and future extreme short-duration rainfall[J]. Nature Geoence, 2017, 10(4):255-259.


Rain gauges and weather radar are the most widely used instruments for near real-time collection of precipitation estimates.

1. Background

(1) Radar image data

• 480 X 480 pixels for HK

(2) Rain-gauges observations

• 123 monitoring stations in HK

One pixel ≈ 1 km2

Wide coverage but not accurate

Accurate but bad coverage


1. Background

Our goal is to do an accurate rainfall prediction with wide coverages.At this stage, we respectively carried out two tasks by using deep learning networks:

Temporal Prediction:

Use deep neural networks for time-series data to predict radar image 𝑿𝑻 in the future.

Spatial Estimation:

Use deep neural networks to estimate the accurate point-wise rainfall at the current timestamp.

(1) Radar Image Data (2) Rain Gauges Observations

• Help to provide regional weather guidance and issue citywide rainfall alerts.

• Help to quantitatively estimate theeffect of rainfall on a location

1 Background



4 Future Work

| CONTENTS


(1) Numerical Weather Prediction (NWP)

• These models build huge framework based on physics equations related to rainfall, to predict

various weather data step by step.

• Typical models include WRF (weather research & forecasting) model.

2. Temporal Prediction – Traditional Methods

Traditional methods:

However, WRF model generates accurate results for other weather data such as temperature and

pressure, but bad results for rainfall (even worse than using mean value as prediction result)


[1] Xingjian Shi, Zhourong Chen, et al: Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting. NIPS 2015: 802-810[2] Yunbo Wang, Mingsheng Long, Jianmin Wang, Zhifeng Gao, Philip S. Yu: PredRNN: Recurrent Neural Networks for Predictive Learning using Spatiotemporal LSTMs. NIPS 2017: 879-888[3] W.C. Woo and W.K. Wong. Application of optical flow techniques to rainfall nowcasting. In the 27th Conference on Severe Local Storms, 2014.


Traditional methods:

(2) Radar Echo Extrapolation

• Radar images of cloud shows high correlation with rainfall.

• Many methods are developed to predict radar image as a replacement of rainfall.

These years, deep learning models such as [1,2] show great effect and outperform other

methods such as ROVER [3] with Variational methods used by HKO.


[1] Xingjian Shi, Zhourong Chen, et al: Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting. NIPS 2015: 802-810[2] Yunbo Wang, Mingsheng Long, Jianmin Wang, Zhifeng Gao, Philip S. Yu: PredRNN: Recurrent Neural Networks for Predictive Learning using Spatiotemporal LSTMs. NIPS 2017: 879-888[3] W.C. Woo and W.K. Wong. Application of optical flow techniques to rainfall nowcasting. In the 27th Conference on Severe Local Storms, 2014.


(1) Numerical Weather Prediction (NWP)

• Typical models include WRF (weather research

& forecasting) model.

(2) Radar echo extrapolation

• Radar images of cloud shows high correlation

with rainfall.

We combine these two, WRF data and radar image, for better rainfall prediction


WRF dataShape: 162 * 213

Interval: 60 min

Scale: real numbers

21

3

4

Radar images Shape: 480 * 480

Interval: 6 min

Scale: 0~255 normalized

21

3

162*213 (HK

island)

60 min

normalized

Radar images Time: future hour

Shape: 162*213

Scale: 0~255 normalized

21

3

We combine these 2, WRF data and radar image, for better rainfall prediction

2. Temporal Prediction – Data Processing


Hourly Radar + WRF to predict radar image of next hour

WRF dataShape: 162 * 213

Interval: 60 min

Scale: real numbers

21

3

4

normalized

QV TD U V 𝑈2 + 𝑉2

AVG AVG AVG AVG AVG

2011 0.393 0.384 0.134 0.182 0.294

2012 0.292 0.291 -0.149 0.174 0.244

2013 0.279 0.281 -0.04 0.175 0.346

2014 0.127 0.136 0.206 0.326 0.346

2015 0.242 0.245 0.24 0.2 0.221

Choose and create WRF data correlated to rainfall.

Result of Pearson Coefficient shows QV and a designed feature (wind speed) are important.

2. Temporal Prediction – Data Processing


Some DL models

• Paper [1] proposes ConvGRU (Convolution GRU) and TrajGRU (Trajectory GRU).• Paper [2] proposes PredRNN.• Paper [3] proposes MIM (memory in memory).

[1] Xingjian Shi, et al.: A Machine Learning Approach for Precipitation Nowcasting. NIPS 2015.[2] Yunbo Wang, et al.: PredRNN: Recurrent Neural Networks for Predictive Learning using Spatiotemporal LSTMs. NIPS 2017.[3] Yunbo Wang, et al.: Memory in Memory: A Predictive Neural Network for Learning Higher-Order Non-Stationarity From Spatiotemporal Dynamics. CVPR 2019.

Problems of these DL models

• Rainfall has physics relationships with other weather data. • Existing works [1,2,3] does not deal with rainfall regarding to its nature of physical phenomenon,

but still treat it as an image processing problem.

2. Temporal Prediction – Current DL Methods


Solution to a physics model

• Previous CNN models modelling non-linearity mostly based on: ReLU with pairwise linear output or Gate functions with bounded output

• But many physics model has complex relationships like 𝑒𝑥, 𝑥4. These features need more powerful operator.

2. Temporal Prediction – Our Model


The Weierstrass Approximation Theorem

• Theorem (Weierstrass Approximation Theorem) (1885). • Let 𝑓 ∈ 𝐶 𝑎, 𝑏 . Given any 𝜖 > 0 there exists a polynomial 𝑝𝑛 of sufficiently high degree 𝑛 for which

𝑓 𝑥 − 𝑝𝑛 𝑥 ≤ 𝜖 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑥 ∈ 𝑎, 𝑏

With polynomial function approximated by transformer, we can approximate given function to any precision.

• 1 transformer layer can generate 𝑓 𝑥 = 𝑎𝑥3 + 𝑏𝑥2 + 𝑐𝑥 + 𝑑• 𝑛 layers generate order of 3𝑛


Solution to a physics model - Transformer


Transformer-based Convolution

𝑅9×𝐷

𝑌𝑅1×𝐷

Each pixel 𝑝1 ∈ 𝑃 (red) is influenced by neighbors 𝑡2 ∈

𝑃𝑛1 (blue)

3X3 cells as example ( 𝑃𝑛1 = 9) Transformer

Merge the functionality of transformer with Convolution for general model usage.



0.3596 0.34960.3565 0.3618

0.2891

0.3191

0.2877 0.28230.3045

0.32720.3533 0.365

0.47

0.5015

0

0.1

0.2

0.3

0.4

0.5

0.6

Input 3 Input 6

Loss (the lower the better)

ConvGRU pure

ConvGRU mix

Tr+GRU

TrGRU

PredRNN

MIM

AVGOurs Ours

2. Temporal Prediction – Results

[1] Xingjian Shi, et al.: A Machine Learning Approach for Precipitation Nowcasting. NIPS 2015.

Loss = 𝑎 ∗ (𝑚𝑠𝑒(𝑤𝑒𝑖𝑔ℎ𝑡𝑒𝑑) + 𝑚𝑎𝑒(𝑤𝑒𝑖𝑔ℎ𝑡𝑒𝑑)), which is a metric for rainfall given by [1]


• 4 baselines are tested for rainfall prediction

• A new module transformer+ is devised. A new operator based on transformer and CNN is devised. 2 new models get state of the art results for rainfall prediction

• The new module performs well on the validation dataset to approximate cubic functions. Our model outperforms CNN with much smaller size

Result Summary

• Properly integrate various data with data processing and suitable model framework can improve the results

• We should design deep learning model according to the nature of tasks, e.g., the complex non-linearity of physics model.

Discussion

2. Temporal Prediction – Conclusions

1 Background



4 Future Work

| CONTENTS


3. Spatial Estimation

• Rain gauges provide accurate measurements at some point locations. • Due to the extreme sparsity, rainfall spatial estimation in areas without rain gauges

has been an important issue.• Task: how to do rainfall estimation for a location without rain gauge?



The most frequently used methods:

Inverse Distance Weighting (IDW) Weights are calculated based on distance

Kriging Geostatistical method Use semivariogram to estimate the spatial

variability, then calculate the weights

Drawbacks:

• Only consider the distance factor• The structure of nodes is ignored

• Subjective Assumptions• The spatial attribute is uniform;• All points (x, y) in the space share the

same expectation 𝑐 and variance 𝜎^2.

Also, it is difficult for them to deal with non-linear real-world situations.



Our Target

Utilize deep learning networks to estimate the spatial distribution of rainfall, and achieve the following advantages:

a) NO subjective statistical assumptions;b) Ability to capture the nonlinear relationship;c) If available, other factors or data can be further added and fused adequately.



Our Target

a) NO subjective statistical assumptions

• Build graphs based on sparse monitoring stations

• Information propagate along the edges

• Make no assumptions about the spatial distribution



Our Target

b) Ability to capture the nonlinear relationship;

• The activation function helps to introduce nonlinear characteristics into the networks.

Different Types of Activation Functions



Our Target

c) If available, other factors or data can be further added and fused adequately.

• If have more meteorological observations (e.g., wind speed, humidity), it is very easy to combine these factors as the node features.

[𝑥1, 𝑥2, 𝑥3, … , 𝑥𝑛]



Two types of nodes:(1) Training nodes (stations);(2) Testing nodes (non-stations).

Geographic relation: Static spatial relationships among nodes,

such as distance, elevation info.

Dynamic matrix: Adaptively learn and fine-tune spatial

relationship.

Our Solution

Geographic relation Dynamic matrix

Fusion

GCN Network



• Timespan: 2009-2015; 3770 valid rainy timesteps in rainstorm events.

• Totally 123 rain gauges in HK.• HK region is subdivided into 12 grids equally.• Sample 25% nodes in each grid as test nodes.• The rest nodes are used for training/calibration.

• IDW: Inverse Distance Weighting• ORK: Ordinary kriging• Ours: our solution

Dataset Splitting and Result Comparison

Dataset Results3.2889

1.1919

2.924

1.0457

2.8671

1.0219

0

0.5

1

1.5

2

2.5

3

3.5

RMSE MAE

IDW

ORK

Ours


3. Spatial Estimation Visualization of Estimated Error Distribution

Accumulative Error

Rainstorm Event:08-17/Jun/2009

▲: train set▼: test set

For each test node, its accumulative error is calculated by:

𝐸 = σ𝑖=0𝑛 𝑦𝑖 − ො𝑦𝑖

Lower Error

𝑦𝑖: real rainfallො𝑦𝑖: estimated rainfall



• Two spatial interpolation methods are tested as baselines

• Our proposed GCN solution can get a better performance than the traditional methods on 2009-2015 dataset including 3770 valid rainy timestamps.

Result Summary

Discussion

• The results show the potential of non-linear neural networks in rainfall spatial estimation.• Merging more data should be explored to further improve performance.

1 Background



4 Future Work

| CONTENTS


4. Future Work

Continue to explore the spatial-temporal characteristics of precipitation, try to provide more accurate precipitation information.

For Temporal PredictionTask: • Gather more types of weather data and adjust current model to improve the

accuracy of rainfall prediction• Apply our model to various physics models to validate its generalization ability

For Spatial Estimation Task: • Combine more weather data, e.g., radar images• Explore the relationship among various data and establish better spatial

relationships dynamically• Further improve the robustness and reliability of our method

Date: Mar. 26, 2021 Thanks!Deep Learning Powered Rainfall Prediction

deep learning powered rainfall prediction

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