Step by Step：Angular Normalization of Daily Night-time Light Data

https://www.un-spider.org/advisory-support/recommended-practices/recommended-pr…
https://www.un-spider.org/node/13569/edit

This Recommended Practice utilizes Python for processing NASA's Black Marble daily night-time light (NTL) data. The procedure involves data filtering, angular normalization to remove viewing zenith angle (VZA) effects, gap-filling, and calculating disaster recovery indices.

1. Data Acquisition:
  • Download the daily at-sensor TOA night-time radiance (VNP46A1) and daily moonlight-adjusted NTL (VNP46A2) from NASA's Black Marble product suite for your study area and timeframe (e.g., 1 month pre-disaster to several months post-disaster).
  • Download the GlobeLand30 land-cover dataset (30m resolution) to identify and extract urban built-up areas (artificial surfaces), as these areas concentrate human activity and artificial light.
 
2. Data Filtering & Quality Control:

To remove low-quality data and non-artificial light, apply the following strict selection criteria to each pixel:

  • Remove pixels with a solar zenith angle less than 108 degrees to eliminate solar illumination interference.
  • Filter out cloud-contaminated pixels using the QF cloud mask from the VNP46A2 product.
  • Perform a secondary selection using the mandatory quality flag to remove abnormal values.
  • Remove pixels with a moon illumination fraction above 60% to precisely identify cloud-polluted pixels.

3. Spatial Smoothing:
  • Apply a 3 × 3 moving window to calculate the average radiance. This alleviates geometric errors and image noise in the night-time light images.
Step 1: Angular Normalization


Satellite-observed NTL radiance has a strong nonlinear relationship with the Viewing Zenith Angle (VZA), causing significant time-series fluctuations. This step normalizes the radiance as if the VZA is always zero.


1. Principle:


The angular normalization algorithm is designed to remove the variations in observed night-time light radiance derived from changes in the Viewing Zenith Angle (VZA). Previous research identified a strong nonlinear relationship between night-time light radiance and VZA, which can be expressed as:

Figure 1

 

Where  denotes the VZA,  denotes the night-time light radiance, and , , and  represent the coefficients. This model is called the Zenith-Radiance Quadratic (ZRQ) model.
The purpose of the normalization algorithm is to estimate the radiance time series assuming the VZA is equal to zero over time. Based on previous studies, we assume that the anisotropy of night-time light radiance remains constant if the land use of an area does not change over a short period. Therefore, the radiance in all directions will change by the same percentage even if the total light emission of the region changes. Based on this basic hypothesis, the radiance of night-time light over a period is modeled as:

 

Figure 2

 

Where R (Z,t) epresents the night-time light radiance under the VZA of Z at moment t , c (t)  is the actual radiance at moment t assuming the VZA is zero, (α'Z2 + b Z + 1) is the function changing with VZA, and α'  and b'  are the coefficients. This model effectively decomposes the satellite-observed time series radiance dynamic into two components: the real light emission changes (represented by the radiance at a VZA of zero, c(t) ), and the VZA-change-derived radiance observation due to the anisotropy.


2. Implementation Steps:


1) Define the Objective Function: The algorithm assumes that if land use remains unchanged, the anisotropy of NTL radiance remains consistent over a short period. The goal is to estimate the time series radiance c(t) at a VZA of zero. The objective function minimizes the correlation (R2) between the angle-normalized time series and the VZA using a Zenith-Radiance Quadratic (ZRQ) model.


2) Optimize and Solve:

  • Utilize the Nelder-Mead algorithm to minimize the objective function and solve for the required coefficients.
  • In Python, this can be implemented using the scipy.optimize.fmin package.

 

Fig. 1. The pixels of night-time light time series curves before and after the angular normalization in two different regions: (a) Arecibo; (b) Bayamon. Image Source: Jia et al. 2023 https://doi.org/10.1016/j.jag.2023.103359
Fig. 1. The pixels of night-time light time series curves before and after the angular normalization in two different regions: (a) Arecibo; (b) Bayamon.
Image Source: Jia et al. 2023 https://doi.org/10.1016/j.jag.2023.103359 

 

Step 2: Time Series Gap-Filling


After obtaining the angle-normalized time series T, we need to use an additive time series model named Prophet to gap-filling the missing data which makes the time series more complete.


The Prophet model is a generalized time series model that can handle various types of patterns, including seasonal and non-seasonal characteristics, which mainly includes the trend term, seasonal term, and the error term. The three terms are optimized by the L-BFGS algorithm to obtain the fitted value. We use the real observation data to fit the time series, and only fill in the fitted values of night-time light radiance at the missing moments thereby completing the time series gap-filling.


Due to the strict filtering criteria in the pre-processing stage (e.g., removing cloud or moonlight contaminated pixels), the resulting time series will have missing data points.

  • Apply the Prophet additive time series model to fill in the missing gaps.
  • The Prophet model handles seasonal and non-seasonal characteristics by optimizing trend, seasonal, and error terms using the L-BFGS algorithm. Fill in the fitted values only at the missing moments to complete the time series.

Step 3: Estimation of Power Restoration

Once the stable and continuous time series is generated, it can be used to assess disaster damage and track power recovery.


1. Power Supply Index (PSI): Calculate the PSI to quantify the current power supply relative to the pre-disaster baseline.

Figure 3
(Where TNLi  is the total night-time light radiance at time i, and TNLpre-disaster  is the stable total night-time light before the disaster).

 

2. Power Restoration Index (PRI): Calculate the PRI to measure resilience and the chronological progression of recovery from the maximum point of damage.

 

(Where represents the total night-time light at the most damaged moment).
(Where TNLdarkest  represents the total night-time light at the most damaged moment).

 

 

Fig. 2. Estimation of power supply index in Puerto Rico
Fig. 2. Estimation of power supply index in Puerto Rico: (a) non-angle-normalized time series estimation; (b) angle-normalized time series estimation.
Image Source: Jia et al. 2023 https://doi.org/10.1016/j.jag.2023.103359