=Paper=
{{Paper
|id=Vol-3026/paper11
|storemode=property
|title=Rainfall Prediction in Vietnam Using Grey Forecasting Model
|pdfUrl=https://ceur-ws.org/Vol-3026/paper11.pdf
|volume=Vol-3026
|authors=Nguyen-Nhu-Y Ho,Phuong Mai Nguyen,Phuong-Huyen Do,Huong-Trang Pham,Nam D. Vo
}}
==Rainfall Prediction in Vietnam Using Grey Forecasting Model==
https://ceur-ws.org/Vol-3026/paper11.pdf
Rainfall Prediction in Vietnam
Using Grey Forecasting Model⋆
Nguyen-Nhu-Y Ho1[0000−0002−7188−7927] , Phuong Mai
⋆⋆
Nguyen1, [0000−0002−2704−9707]
, Phuong-Huyen Do1 , Huong-Trang Pham1 , and
Nam D. Vo2[0000−0001−5469−5707]
1
International School, Vietnam National University, Hanoi, Vietnam
hngny@vnu.edu.vn; mainp@vnu.edu.vn; huyendp@isvnu.vn; trangph@vnu.edu.vn
2
The University of Danang, Danang, Vietnam
vdnam@ac.udn.vn
Abstract. Vietnam is an agriculture-based country that is heavily af-
fected by the climate change when El Niño is causing a significant impact
on the rainfall of the country. In such a context, it becomes harder to
predict the rainfall without applying modern methods and techniques.
Thus, Vietnamese farmers have to deal with increasing difficulties in
making choices of crops to grow, and irrigation plans for higher output
and income if they still base on their old cultivation habit and subjec-
tive prediction of climate condition. Regarding the mentioned issue, this
paper modifies an integrative framework that uses Grey (1;1) model to
forecast the rainfall in Vietnam. Data of the rainfall amount from 2017 to
2020 in 15 meteorological regions throughout the country were collected
to put into the Grey (1,1) forecasting model. The computation results
show the total rainfall prediction for four consecutive years from 2021
to 2024 in 15 selected regions. These results will be useful for farmers
in making their cultivation choices and other governing agencies to alter
the agriculture related policies.
· ·
Keywords: Rainfall prediction Grey model Forecasting model.
1 Introduction
Rainfall is significant for agriculture as well as human beings and animals. Agri-
culture production is highly dependent upon precipitation, which falls in the
form of rain [7]. Dependence on uncertain rainfall and exposure to unmitigated
climate risks are major obstacles to efforts to intensify agricultural production
⋆
Copyright © by the paper’s authors. Use permitted under Creative Commons Li-
cense Attribution 4.0 International (CC BY 4.0). In: N. D. Vo, O.-J. Lee, K.-H. N.
Bui, H. G. Lim, H.-J. Jeon, P.-M. Nguyen, B. Q. Tuyen, J.-T. Kim, J. J. Jung, T. A.
Vo (eds.): Proceedings of the 2nd International Conference on Human-centered Arti-
ficial Intelligence (Computing4Human 2021), Da Nang, Viet Nam, 28-October-2021,
published at http://ceur-ws.org
⋆⋆
Correspoding author: mainp@vnu.edu.vn
Rainfall Prediction in Vietnam Using Grey Forecasting Model 101
and enhance rural livelihoods sustainably, and causes negative impacts. Accord-
ing to Purdy et al., in areas with rainy and dry seasons, soil nutrients diminish
and erosion increases during the rainy season [9]. The previous dry season leads
to food shortages in the rainy season, as the crops have yet to mature. In addi-
tion, excessive rain during short periods of time often causes flash floods. Climate
shocks such as drought and floods lead not only to the loss of life but also the
long-term loss of livelihood through loss of productive assets, impaired health
and destroyed infrastructure. It is insisted that the uncertainty associated with
climate variability is a disincentive to investment and adoption of agricultural
technologies and market opportunities, prompting the risk-averse farmer to favor
precautionary strategies that buffer against climatic extremes over activities that
are more profitable on average [6,5]. To the degree that climatic uncertainty ad-
versely impacts farmer livelihoods, forecast information that reduces uncertainty
becomes increasingly important. This type of information enables farmers to in-
tensify production, replenish soil nutrients, motivates them to adopt improved
technology to more effectively protect their families and farms against the long-
term consequences of adverse extremes [1,4].
Vietnam is an agricultural-based country with a long history dating back
to a thousand years ago. Agriculture is contributing about 20% to the national
GDP. As an agricultural country, most of the poor live on agriculture and fish-
ing. However, the cultivation practices in many rural areas are still straightfor-
ward without applying high technologies. Consequently, agriculture production
depends heavily on the climate. Notably, Vietnam is assessed by the United
Nations Development Organization as one of the top five countries in the world
that is most directly vulnerable to climate change. The impacts of climate change
such as sea-level rise, floods, droughts, salt-water intrusion, and extreme weather
are becoming more and more apparent, causing damage to agriculture and Viet-
nam’s economy in general.
For example, according to the analysis of the World Resources Institute on
the impact of floods on GDP, Vietnam ranked fourth out of 164 surveyed coun-
tries in terms of the severe harm of floods to the whole economy. Floods are
estimated to cause a loss of 2.3% of Vietnam’s GDP every year. Moreover, salt-
water intrusion reduces the area of arable farming land, from which the coefficient
of land use may reduce from 3-4 times/year to 1-1.5 times/year. According to
research results of the Institute of Agricultural Environment (Ministry of Agri-
culture and Rural Development), climate change reduces the yield of some key
crops. Specifically, Spring rice yield will decrease by 0.41 tons/ha in 2030 and
0.72 tons in 2050. Maize yield is likely to fall by 0.44 tons/ha in 2030 and 0.78
tons in 2050. It is forecasted that by 2100, the Mekong Delta is at risk of being
flooded with 89,473 hectares, which means that this area will lose about 7.6
million tons of rice/year if the sea level rises 100 cm. At that time, Vietnam is
at risk of severe food shortages and poverty.
In addition, the increase of storms also decreases the GDP growth rate of
Vietnam. If the average growth rate is 5.4% annually, the growth rate affected
by hurricanes will be about 5.32% to 5.39%. The sea-level rise scenarios show
102 Ho et al.
that even the mildest impact level will cause GDP from 2046 to 2050 to decrease
by 0 to 2.5%. Meanwhile, because Vietnam’s GDP by 2050 is forecasted to be
more than 500 billion USD, the value of the damage caused by climate change is
about 40 billion USD. This damage is relatively significant but can be minimized
with appropriate adaptation policies.
In this regard, it is essential to proactively assess and forecast the fluctuation
of several critical elements in the agriculture sector, such as rainfall, to respond
and develop a suitable and sustainable agriculture sector promptly. Hence, it
is suggested using algorithms to predict seasonal rainfall a part of the solu-
tion for hydro-meteorological forecasting. Therefore, this paper proposes a mod-
ified framework using the Grey forecasting model to predict future precipitation
trends of 15 meteorological regions in Vietnam from 2021 to 2024.
2 Methodology
2.1 Grey Forecasting Generation Theory
In the agriculture sector, forecasting is an essential determinant of operational
performance. A dynamic Grey forecasting model is applied in this paper to im-
prove forecasting accuracy. The Grey system theory, established by Deng in
1982, is a new method that focuses on the study of problems involving small
samples and poor information [2]. Grey forecasting GM(1,n) is the most widely
used model. Grey theory is a truly multidisciplinary and generic theory dealing
with systems characterized by imperfect information or for which information is
lacking. The fields covered by Grey theory include systems analysis, data process-
ing, modeling, prediction, decision-making, and control. Grey forecasting models
have been extensively used in many applications. The GM(1, 1) is one of the most
frequently used Grey forecasting models. This model is a time series forecasting
one, encompassing a group of differential equations adapted for parameter vari-
ance rather than a first-order differential equation. Its difference equations have
structures that vary with time rather than being general difference equations.
Consequently, Grey forecasting model is a good tool for predicting the values of
the future mutual relationship among these factors based on a small amount of
data [8].
GM(1,1) is the central model that has been most widely employed, and dis-
crete Grey models are a class of new models we initially developed [8]. Let
X (0) = x(0) (1), x(0) (2), · · · , x(0) (n) be a sequence of raw data. Denote its
accumulation-generated sequence by X (1) = x(1) (1), x(1) (2), · · · , x(1) (n) . Then
X (0) (k) + ax(1) (k) = b (1)
is refered to as the original form of the GM(1,1) model, where the symbol
GM(1,1) stands for ”first-order Grey model in one variable”.
Let Z (1) = z (1) (1), z (1) (2), · · · , z (1) (n) be the sequence generated from X (1)
by the adjacent neighbor means. That is,
Rainfall Prediction in Vietnam Using Grey Forecasting Model 103
(1) 1 (1) (1)
z (k) = x (k) + x (k − 1) , k = 2, 3, · · · , n (2)
2
Then
x(0) (k) + az (1) (k) = b (3)
is refered to as the basic form of the GM(1,1) model.
Theorem 1. Let X (0) , X (1) , and Z (1) be the same as above accept that X (0) is
non-negative. If â = (a, b)T is sequence of parameter, and
x(0) (2)
x(0) (3)
Y = .. , (4)
.
x(0) (n)
−z (1) (2) 1
−z (1) (3) 1
B= , (5)
..
. 1
−z (1) (n) 1
a
â = (6)
b
the least squares estimate sequence of the GM(1,1) model Eq.(3) satisfies â =
(B T B)−1 B T Y .
Continuing all the notations from Theorem 1, if [a, b]T = (B T B)−1 B T Y , then
d(x)1 1
dt + ax = b is a whitenization equation of the GM(1,1) model in the Eq.(3).
Formula to solve the values a and b are as follow
Pn (1)
Pn (0) n
(k) − (n − 1) × k=2 z (1) (k)x(0) (k)
P
k=2 z (k) × k=2 x
a= (7)
(1) (k) 2
Pn Pn
(n − 1) k=2 z (1) (k)2 − k=2 z
Pn (0)
Pn (1)
Pn Pn
k=2 x (k) × k=2 z (k 2 ) − k=2 z
(1)
(k) × k=2 z
(1)
(k)x(0) (k)
b= Pn Pn 2 (8)
(n − 1) (1) (k)2 − (1) (k)
k=2 z k=2 z
The time response sequence of the GM(1,1) model in the Eq.(3) is given
below
b −ak b
x̂(1) (k + 1) = x(0) (1) − e + , k = 1, 2, · · · , n (9)
a a
104 Ho et al.
The parameters (−a) and b of the GM(1,1) model are referred to as the de-
velopment coefficient and Grey action quantity, respectively. The former reflects
the development states of x̂(1) and x̂(0) . In general, the variables that act upon
the system of interest should be external or pre-defined. Because GM(1,1) is a
model constructed on a single sequence, it uses only the behavioral sequence
(or referred to as output sequence or background values) of the system without
considering any externally acting sequences (or referred to as input sequences,
or driving quantities). The Grey action quantity in the GM(1,1) model is de-
rived from the background values. It reflects changes contained in the data, and
its exact intention is Grey. This quantity realizes the extension of the relevant
intention. Its existence distinguishes Grey systems modeling from general input-
output modeling. It is also a vital test stone of separating the thoughts of Grey
systems and those of Grey boxes.
2.2 Valuation performance
Regarding the valuation performance of the volatility model for forecasting, there
are some common approaches. This study adopted precipitation to evaluate the
performance of the Grey rainfall forecasting model [8]. Model characteristics
include periodicity, randomness, and tendency. To get the trend of the series
and the context of the development of the natural disasters, this study, apart
from improving the background value by integrating, has improved the accuracy
by correcting the model’s periodical errors. The MAPE is defined as follows
n (0) (0)
100% X x(k) − x̂(k)
M AP E = (0)
, (10)
n x
k=2 (k)
(0) (0)
where x(k) and x̂(k) is the actual value and forecast one in time period k, respec-
tively. The grade of MAPE is devided into four levels.
Table 1. The grade of MAPE
MAPE ≤10% 10%-20% 20%-50% ≥50%
Grade levels Excellent Good Qualified Unqualified
Second, the error of total cumulative rainfall (ETCR) is defined as
Pn (0) Pn (0)
k x(k) − k x̂(k)
ET CR = Pn (11)
k x(k)
A more accurate forecast can be obtained when ETCR is approximately zero.
Third, the relative root means square error (RMSE) is defined as
Rainfall Prediction in Vietnam Using Grey Forecasting Model 105
v
uP h i2
u n (0) (0) (0)
t k=1 x(k) − x̂(k) /x(k)
RM SE = (12)
n
A more accurate forecast can be obtained when RMSE is approximately zero.
Fourth, the coefficient of efficiency (CE) is defined as
2
Pn (0) (0)
k=1 x(k) − x̂(k)
CE = 1 − P 2 (13)
n (0) (0)
k=1 x(k) − x̄(k)
Moreover, the coefficient of correlation (CC) is defined as
Pn (0) (0)
(0) (0)
k=1 x (k) − x̂ (k) x̂ (k) − x̄ (k)
CC = r (14)
Pn (0) (0)
P
n
(0) (0)
k=1 x (k) − x̄ (k) × k=1 x̂ (k) − x̄ (k)
3 Results and Discussion
Agriculture production in Vietnam is highly dependent upon precipitation, which
falls in the form of rain. We used GM(1,1) model for predicting the real value
of rainfall in Vietnam based on precipitation data from 2017 to 2020. The data
were collected from fifteen meteorological regions located throughout Vietnam.
These meteorological regions include 6 ones in the North (Lai Chau, Son La,
Tuyen Quang, Ha Noi, Quang Ninh, Nam Dinh), 4 ones in the Central (Vinh,
Hue, Da Nang, Quy Nhon), 2 ones in the Highland (Pleiku, Da Lat), and 3 ones
in the South (Nha Trang, Vung Tau, Ca Mau). An explanation follows.
The sequence of raw data X (0) = x(0) (1), x(0) (2), x(0) (3), x(0) (4) = (2618.7,
2656.6, 2267.2, 2295.1) simulate the original sequence X (0) by respectively using
the following three GM(1,1) models and compare the simulation accuracy:
From Eq.(3), we compute the accumulation
generation of X (0) as follows
(1) (1) (1) (1) (1)
X = x (1), x (2), x (3), x (4) = (2618.7, 5275.3, 7542.5, 9837.6).
(0)
x (k)
We check the quasi-smoothness from the class ratio σ (1) (k) = x(1) (k−1)
, it
follows that σ (1) (2) = 0.503, σ (1) (3) = 0.301, σ (1) (4) = 0.233. So, the condi-
tion to satisfy for k > 3, σ (1) (k) ∈ [0.5; 1] with σ = 0.5 and it is sufficient
and necessary condition to ensure that the accumulate generating opera-tion
(AGO) algorithm coverges. This result is the main contribution of grey class
ratio. It not only makes the grey prediction model smooth, but also increases
the accuracy of predicted values. Hence, according to above, mentioned result,
it is concluded that the criteria which is derived in this section is reasonable
formula and can be widely used in the field of GM (1,1) file. The law of quasi-
exponentially the condition of quasi-smoothness is stratified. Thus, we can es-
tablish a GM(1,1) model for X (1) . Let Z (1) = z (1) (1), z (1) (2), · · · , z (1) (n) be
the sequence generated from X (1) by the adjacent neighbor means sequence
106 Ho et al.
Z (1) = z (1) (1), z (1) (2), z (1) (3), z (1) (4) = (3947, 6408.9, 8690.05). In addition,
matrix B constant vector YN are accumulated as follows
−3947 1
B = −6408.9 1 , (15)
−8690.05 1
2656.6
YN = 2267.2 (16)
2295.1
.
By using the least square estimation, we obtain the sequence of parameters
â = [a, b]T . Then we use (7) and (8) to calculate the parameter:
∗ a = 19045.95×7218.9−(4−1)44960392.035
(4−1)×132169777.2125−(19045.95)2 = 0.0772
7218.9×132169777.2125−19045.95×44960392.035
∗ b= (4−1)×132169777.2125−(19045.95)2 = 28970.31
0.0772
Then â = (B T B)−1 B T Y = , hence we find values of a=0.0772 and
2897.03
b=28970.31.
(1)
We establish the following model dxdt − 0.00768x(1) = 399.433 and building
the prediction equation time response form x̂(k + 1) = x(0) (1) − ab e−a(k) + ab =
−34908e−0.772 + 37526.3. Substitute different values of k into the equation
∗ k = 1X (1) (1) = 2618.7
∗ k = 2X (1) (2) = 5211.8
∗ k = 3X (1) (3) = 7612.1
∗ k = 4X (1) (4) = 9833.7
∗ k = 5X (1) (5) = 11890.1
∗ k = 6X (1) (6) = 13793.6
∗ k = 7X (1) (7) = 15555.4
∗ k = 8X (1) (8) = 17186.3
Compute the simulated values of X (0) the original series according to the
accumulated generating operation of by using x̂(0) (k + 1) = α(1) x̂(01) (k + 1) −
x̂(1) (k):
∗ X (0) (1) = x(1) (1) = 2618.7 forecast for the year 2017
∗ X (0) (2) = x(1) (2) − x(1) (1) = 2593.1 forecast for the year 2018
∗ X (0) (3) = x(1) (3) − x(1) (2) = 2400.2 forecast for the year 2019
∗ X (0) (4) = x(1) (4) − x(1) (3) = 2056.4 forecast for the year 2020
∗ X (0) (5) = x(1) (5) − x(1) (4) = 1903.4 forecast for the year 2021
∗ X (0) (6) = x(1) (6) − x(1) (5) = 1761.8 forecast for the year 2022
∗ X (0) (7) = x(1) (7) − x(1) (6) = 1630.8 forecast for the year 2023
∗ X (0) (8) = x(1) (8) − x(1) (7) = 1630.8 forecast for the year 2024
Rainfall Prediction in Vietnam Using Grey Forecasting Model 107
This study is concerned with the metrics that can accurately reflect the
rainfall measurement during the period 2017 - 2020. According to Ho et al., the
MAPE is to identify the Grey prediction models with good performance; the
ETCR and RMSE represent a quantitative judgment of model performance [5].
The CE is used to measure the similarity between the predicted and observed
accumulated rainfall. The CC is used to measure the correlative relationship
between the predicted and observed accumulative rainfall. When we use the
above computation process, we could get the forecasting results of all the 15
regions from 2021 to 2024. The detailed results are shown in Table 3 and Table
3.
Table 2. The grade of Average MAPEs rainfall of meteorological regions in Vietnam
ETCR RMSE CE MAPE CC
Lai Chau 0.000397 0.035485 0.788485461 0.21% 0.2927
Son La 0.000789 0.069285 0.516938651 0.16% 0.0571
Tuyen Quang 0.003096 0.100293 0.645361493 0.41% 0.08
Ha Noi 0.000838 0.013321 0.98 0.42% 0.0697
Quang Ninh 0.000662 0.12145 0.279955058 0.36% 0.212
Nam Dinh 0.000525 0.045339 0.822012083 0.33% 0.0632
Vinh 0.006107 0.116268 0.824307146 0.24% 0.0802
Hue 0.000741 0.024885 0.911553061 0.06% 0.2791
Da Nang 0.00048 0.026752 0.948342121 0.23% 0.112
Quy Nhon 0.001358 0.006221 0.997702553 0.16% 0.0592
Pleiku 0.0003 0.101836 0.479397367 0.36% 0.1417
Da Lat 8.08E-07 0.027265 0.507316817 0.45% 0.0981
Nha Trang 0.000166 0.165978 0.518417604 0.28% 0.0474
Vung Tau 5.57E-05 0.016562 0.885136372 0.25% 0.045
Ca Mau 0.000543 0.009087 0.978981993 0.25% 0.0987
Average 0.0011 0.059 0.739 0.00% 0.116
Table 3 shows that several requirements of the model accuracy are met such
as residual error (MAPE): 0.0038%, ETCR: 0.0011, RMSE: 0.059, CE: 0.73, and
CC: 0.116. The above statistics confirm the efficiency of the proposed forecasting
model that the average residual error was smaller than 10%. This result means
the forecasting process is excellent, so it strongly confirms that the GM(1,1)
model provides a highly accurate prediction. Therefore, we select MAPE to
calculate the error for this rainfall forecast model in this study. Then the results
of rainfall prediction using the Grey forecasting method are presented in Table
3 below.
As shown in Table 3, among the 15 regions, 5 regions, which are Son La,
Tuyen-Quang, Da Lat, Nha Trang and Ca Mau, are expected to have annual rain-
fall increase through the upcoming 4 years. Tuyen Quang province will have the
highest increase of rainfall, followed by Ca Mau province and Son La province.
While the 10 remaining regions will suffer from a significant decrease of rainfall
108 Ho et al.
Table 3. Forecast of rainfall in Vietnam from 2021 to 2024
2021 2022 2023 2024 Gap between 2024 and 2021
Lai Chau 2056.416 1903.449 1761.861 1630.805 -425.611
Son La 1883.146 2055.677 2244.016 2449.609 566.463
Tuyen Quang 2411.015 2828.856 3319.11 3894.327 1,483.31
Ha Noi 1324.904 1171.5 1035.858 915.922 -408.982
Quang Ninh 1972.19 1814.269 1668.994 1535.351 -436.839
Nam Dinh 1253.402 1109.251 981.677 868.776 -384.626
Vinh 929.731 680.012 497.367 363.778 -565.953
Hue 1928.086 1727.516 1547.81 1386.799 -541.287
Da Nang 1737.015 1568.951 1417.148 1280.032 -456.983
Quy Nhon 1146.694 967.825 816.857 689.438 -457.256
Pleiku 1608.518 1408.192 1232.814 1079.279 -529.239
Da Lat 2004.291 2012.19 2020.119 2028.08 23.789
Nha Trang 1361.24 1413.866 1468.527 1525.301 164.061
Vung Tau 1257.412 1217.769 1179.377 1142.194 -115.218
Ca Mau 2484.71 2706.104 2947.225 3209.831 725.121
until 2024. Nota-bly, Vinh city will experience the biggest shortage of rainfall as
the predicted rainfall in 2024 will be approximately one third of that in 2021.
The estimated rainfall volume in the period from 2021 to 2024 of these 15
regions will serve as an important input for farmers and the governing agencies in
agriculture sector to formulate contingency plans to leverage the risks of rainfall
fluctuation.
4 Conclusion
Quantitative precipitation forecast (QPF) is one of the most important issues
for the meteorological community. Many efforts had been spent on analyzing
the capability of the numerical model in providing QPF. For example, Emerton
et al. evaluated the performance of the Regional Spectral Model (RSM) devel-
oped at the National Centers for Environmental Prediction (NCEP) in providing
quantitative precipitation forecasts for the Tennessee and Cumberland River Wa-
tersheds, USA [3]. They found that the model’s performance was more accurate
than the traditional forecasting models. However, the QPF performance of RSM
for Williamson was relatively unsatisfactory [10].
This study modified an integrated framework for the rainfall forecasting
model using a real-time flow updating algorithm. Applying GM(1,1) to fore-
cast short-term rainfall growth rates can achieve excellent prediction. GM(1,1)
can estimate the residual values and then use MAPE, RSME, CE, and CC
to calculate the valuation performance. The result of this study is essential in
forecasting the natural disasters risk index. It may be concluded that effective
rainfall is directly proportional to consumptive use, water storage capacity, ir-
rigation application and seepage and percolation losses. Policymakers may use
Rainfall Prediction in Vietnam Using Grey Forecasting Model 109
these results to formulate suitable policies towards a sustainable agriculture sec-
tor. The prediction in this study indicates that the applied Grey model process
will help the small farming households reduce the risks and gain benefits from
seasonal forecasts of the rainfall.
This study still has some limitations. Daily and monthly precipitation data
in Vietnam are not available so that we cannot compute the expected rainfall
on the daily or monthly basis. We have just estimated the total rainfall amount
in a year, but have not predicted the amount of rainfall for each month or each
day. For future studies, we may apply different forecasting models that can be
used to optimal forecasting value of the rainfall and also other natural disasters
risk index in the future.
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