# US 2025/0093549 A1 · Method for quantifying structural feature forecast error of meteorological element based on graphical similarity

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- Number: US 2025/0093549 A1
- Document ID: US20250093549A1
- Status: Published application
- Kind: A1
- Application number: 18/641,382
- Filed: 2024-04-21
- Published: 2025-03-20
- Earliest claimed: 2023-09-20
- Assignees: Nanjing Joint Institute for Atmospheric Sciences
- Applicants: Nanjing Joint Institute for Atmospheric Sciences
- Inventors: Xiyu MU; Guoqing LIU; Hao CHENG; Qi XU; Mingjian ZENG; Kan DAI; Hao YAN; Shuqi YAN; Huadong YANG; Hao WU; Yan ZENG
- Web page: https://patentgrep.com/patent/US20250093549A1

## CPC

- G01W 1/02: Instruments for indicating weather conditions by measuring two or more variables, e.g. humidity, pressure, temperature, cloud cover or wind speed (G01W1/10 takes precedence)
- G01W 1/10: Devices for predicting weather conditions (computers per se G06; display devices G09)
- G06F 17/18: for evaluating statistical data {, e.g. average values, frequency distributions, probability functions, regression analysis (forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04)}
- G01W 2201/00: Weather detection, monitoring or forecasting for establishing the amount of global warming
- Y02A 90/10: Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation
- G01W: METEOROLOGY (radar, sonar, lidar or analogous systems, designed for meteorological use G01S13/95, G01S15/88, G01S17/95)
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- Y02A: TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE

## Abstract

A method for quantifying a structural feature forecast error of a meteorological element based on a graphical similarity is based on the concept of graphical similarity to propose a normalized evaluation technique for a forecast error of a scalar meteorological element such as rainfall, radar reflectivity, temperature, visibility, or wind speed. The method can objectively and truly reflect the true capability of forecasting the meteorological element such as precipitation.

## Claims

### Claim 1

A method for quantifying a structural feature forecast error of a meteorological element based on a graphical similarity, comprising the following steps:
S1: defining a structural feature of a meteorological element field;
defining an overall structural feature d of the meteorological element field as an area S of a spatial range covered by the meteorological element, a total numerical size R of the meteorological element in a target region, and a structure H of the meteorological element;
α
→
=
[
S
,
R
,
H
]
(
1
)
wherein, {right arrow over (α)} denotes the overall structural feature of the meteorological element field;
S2: calculating a total amount error and a total area error of the meteorological element;
E
R
=
|
RT
(
f
)
(
t
)
-
RT
(
o
)
(
τ
)
|
max
⁢
(
RT
(
f
)
(
t
)
,
RT
(
o
)
(
τ
)
)
(
2
)
E
S
=
|
ST
(
f
)
(
t
)
-
ST
(
o
)
(
τ
)
|
max
⁢
(
ST
(
f
)
(
t
)
,
RT
(
o
)
(
τ
)
)
(
3
)
wherein, RT(f)(t) denotes a total amount of a forecasted meteorological element field at a time t; RT(0)(τ) denotes a total amount of an observed meteorological element field at a time τ; ST(f)(t) denotes a total area covered by the forecasted meteorological element field at the time t; and ST(0)(τ) denotes a total area covered by the observed meteorological element field at the time τ;
S3: calculating a structural error of the meteorological element field;
firstly, calculating, based on a probability density function, a structural feature p(f)(ζf,t) of the forecasted meteorological element field and a structural feature p(0)(ζ0,τ) of the observed meteorological element field according to Eqs. (4) and (5), respectively;
{
p
(
f
)
(
ξ
f
,
t
)
=
H
(
f
)
(
ξ
f
,
t
)
ξ
f
=
(
R
f
-
R
min
f
)
/
(
R
max
f
-
R
min
f
)
∈
[
0
,
1
]
(
4
)
wherein, H(f)(ζf,t) denotes a probability density function for the forecasted target element field at the time t; ζf denotes a coefficient of the meteorological element after the forecasted meteorological element field is normalized; and ζf takes a value of 0-1;
{
p
(
0
)
(
ξ
f
,
t
)
=
H
(
0
)
(
ξ
0
,
t
)
ξ
0
=
(
R
0
-
R
min
0
)
/
(
R
max
0
-
R
min
0
)
∈
[
0
,
1
]
(
5
)
wherein, H(0)(ζ0,t) denotes a probability density function for the observed target element field at the time t; ζ0 denotes a coefficient of the meteorological element after the observed meteorological element field is normalized; and ζ0 takes a value of 0-1; and
secondly, measuring, based on a Kullback-Leibler (KL) divergence algorithm (6), a similarity EH between the structural feature of the forecasted meteorological element field and the structural feature of the observed meteorological element field;
E
H
=
∑
ξ
f
p
(
f
)
(
ξ
f
,
t
)
⁢
log
⁢
p
(
f
)
(
ξ
f
,
t
)
p
(
o
)
(
ξ
o
,
t
)
(
6
)
S4: calculating a similarity between the target element field and the observed element field;
calculating the similarity E between the forecasted meteorological element field and the observed element field according to Eq. (2);
E
=
E
R
+
E
S
+
E
H
(
7
)
wherein, ER denotes the total amount error of the meteorological element; ES denotes the total area error of the meteorological element; and EH denotes the structural error of the meteorological element.

### Claim 2 (depends on 1)

The method for quantifying the structural feature forecast error of the meteorological element based on the graphical similarity according to claim 1, wherein the method further considers a time error Et between the forecasted meteorological element field {right arrow over (α)}(f)(t) and the observed meteorological element field {right arrow over (α)}(0)(τ) at consecutive times, specifically as follows:
firstly, calculating, within a time range of t=τ±2Δt, the similarity E(t,τ) between the forecasted meteorological element field {right arrow over (α)}(f)(t) at each time and the observed element field {right arrow over (α)}(0)(τ) at the time τ according to steps S1 to S4; calculating the time error as τ−t, wherein when a similarity E(t,τ) reaches a maximum value, the time corresponding to the forecasted meteorological element field is t; and
normalizing according to Eq. (8) to acquire a normalized time error Et;
E
t
=
|
τ
-
t
|
2
⁢
Δ
⁢
t
(
8
)
wherein, Et denotes the time error between the forecasted meteorological element field {right arrow over (α)}(f)(t) and the observed meteorological element field {right arrow over (α)}(0)(τ) at the consecutive times; and Δt denotes a time interval of the forecasted meteorological element field; and
secondly, acquiring an overall error E between the forecasted meteorological element field and the observed meteorological element field, wherein E=ER+ES+EH+Et.

### Claim 3 (depends on 1)

The method for quantifying the structural feature forecast error of the meteorological element based on the graphical similarity according to claim 1, wherein the meteorological element comprises rainfall, radar reflectivity, temperature, visibility, and wind speed.