Distributed Sensor Network for meteorological observations and numerical weather Prediction Calculations
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A. Vas et al. / Carpathian Journal of Electronic and Computer Engineering 6/1 (2013) 56-63 56
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Distributed Sensor Network for meteorological
observations and numerical weather Prediction
Calculations
Ádám Vas Ádám Fazekas
University of Debrecen, Faculty of Science and Technology, University of Debrecen, Faculty of Informatics,
Department of Meteorology Department of Informatics Systems and Networks
Debrecen, Hungary Debrecen, Hungary
vas.adam@inbox.com fazekas.adam@inf.unideb.hu
Gábor Nagy, László Tóth
SciTech Műszer Kft.
Debrecen, Hungary
nagyg2000@t-online.hu, laszlo.toth@scitechmuszer.com
Abstract—The prediction of weather generally means the one. Apparently, finding a perfect analogue for an event in the
solution of differential equations on the base of the measured past had low probability which made this technique difficult to
initial conditions where the data of close and distant neighboring use.
points are used for the calculations. It requires the maintenance
of expensive weather stations and supercomputers. However, if The first weather prediction based on physical equations
weather stations are not only capable of measuring but can also and numerical calculation was made by Richardson [3] in the
communicate with each other, then these smart sensors can also first decades of the 20th century. The complexity of numerical
be applied to run forecasting calculations. This applies the weather prediction models started to increase significantly
highest possible level of parallelization without the collection of when the Electronic Numerical Integrator and Computer
measured data into one place. Furthermore, if more nodes are (ENIAC) was announced and the modeling work by J.
involved, the result becomes more accurate, but the computing Charney, R. Fjørtoft and J. von Neumann (CFvN) [4] started.
power required from one node does not increase. Our Distributed As computers grew in power and capacity, it became possible
Sensor Network for meteorological sensing and numerical to run more complex mathematical models involving denser
weather Prediction Calculations (DSN-PC) can be applied in initial data in space and time [2].
several different areas where sensing and numerical calculations,
even the solution of differential equations, are needed. Since the number of measurement points and observed
parameters nowadays are relatively large and continuously
Keywords— distributed sensor network; meteorological grow, as well as the complexity of the models, the weather
sensing; numerical weather prediction forecasting calculations require more and more expensive
supercomputers, although modern weather sensors are already
I. INTRODUCTION equipped with a digital central unit (microprocessor (µP),
Meteorology is strongly influenced by scientific and microcontroller (µC), Digital Signal Processor (DSP), Field
technological developments, which is especially true in the Programmable Gate Array (FPGA)), which represents a
case of weather forecasting. The improvements of significant computation power currently utilized “only” for
thermodynamics helped to recognize that the solution of filtering the measured values and sending them to a central
equations of hydro- and thermodynamics as well as continuity computer.
with five initial variables (pressure (mbar), temperature (°K),
The central computer could be eliminated or greatly
density (kg/m3), humidity (%), velocity (m/s)) are feasible to
simplified with our method of forecast calculations where the
be used for successful weather forecasting calculations [1],[2].
nodes are connected to each other through the Internet;
However, the fast collection of weather data reports from therefore, it is not needed to collect data and make the
wide areas became possible only after the invention of electric calculation at one location. These nodes can communicate
telegraph in 1835. Because of the lack of known physical and with each other and make numerical finite difference or finite
mathematical models as well as proper computing element calculations based on their close and distant
instruments, forecasting was based on a visual pattern neighbors’ data. This grid itself forms the sensor network and
recognition method where a previous similar weather situation a distributed computing system, which can be used for solving
and the subsequent one were used to predict the upcoming differential equations without using a central computer, so it
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A. Vas et al. / Carpathian Journal of Electronic and Computer Engineering 6/1 (2013) 56-63 57
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can function as a multiprocessor system with extremely high In CFvN calculations the spherical Earth was mapped by
number of computational units, making the highest level of polar stereographic projection onto a rectangular plane (Fig. 2)
parallelization of the calculations possible. with sides of Lx and Ly, then a rectangular grid was created
and defined by the coordinates of
In such a system by increasing the number of nodes for
getting better covered field and therefore more accurate
calculations the computing power required by one node does Lx Ly
x i, y j
not increase, since they use their close and distant neighbors’ p q
data only (Fig. 1). The nodes can also be placed on the board
of moving vehicles i.e. ships and airplanes for monitoring i 0, ..., p; j 0, ..., q
even the vertical parameters.
Our work of developing DSN-PC started five years ago where
[5],[6],[7],[8],[9],[10], and here we present the latest results.
II. THE ENIAC FORECAST AND ITS IMPLEMENTATION ON Lx L y
s (2)
DSN-PC p q
Earlier it was shown that our µC based networked sensor
system is able to do both meteorological sensing and making and s=736 km at the North Pole (494 km at 20°N), λ=8°
calculations simultaneously. These calculations involved of longitude at =45°N.
determining isotherm lines, temperature gradient vectors and
solving the differential equation of heat transfer by applying During the following calculations, according to CFvN, the
finite difference method (FDM) based on communication next notations are used:
between nodes [9]. For demonstrating the functionality and
capability of our method and networked system also for cos
r (3)
simple weather prediction calculations, the well-known first 1 sin
successful 24 hour weather prediction algorithm for large-
scale motions in barotropic atmosphere, developed by CFvN
dr 2
and run on the ENIAC, was applied. Here the CFvN solution m 2 1 r2 (4)
of finite difference linearized barotropic vorticity equations is d 1 sin
also shown. Although it was used for calculating predictions
for the 500 mbar geopotential heights and its input data set 1 r2
differs from that of our DSN-PC stations can provide (ground f 2 sin 2 (5)
level pressure (mbar), temperature (°C) and relative humidity 1 r2
(%)) at the present, by applying CFvN calculations we could
show the capability of our system of realizing such kind of gm 2
calculations. We are working on development of new and h (6)
more sophisticated weather prediction algorithms for DSN- f
PC.
Fig. 1. The conception of DSN-PC sensor network, which forms the necessary grid for numerical calculations by using the nodes of the networked sensor stations
not only for measurements and collection of data but for making numerical calculations in a distributed way. The networked weather stations (nodes) are able to
communicate with their close and distant neighbors through the Internet and solve weather prediction calculations. In the present work we applied FDM on a
rectangular grid (Left) but the calculations can also be done by Finite Elements Method (FEM) on irregular grid (Right).
ISSN 1844 – 9689 http://cjece.ubm.roA. Vas et al. / Carpathian Journal of Electronic and Computer Engineering 6/1 (2013) 56-63 58
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z is the geopotential height of the 500 mbar level. The
°
90 E initial data were taken from the 500 mbar analyses of
°
120 E 60 ° E the U.S. Weather Bureau [4]. In our case the
interpolated data for the initial values of z at the grid
points were taken from [11].
°
150 E 30 ° E
is the absolute vorticity.
the hij and fij parameters are independent of t and have
to be calculated only once for each node.
the Poisson equation:
° °
° 0° 20 N 40 N 60 ° N 80 ° N °
180 E 0
z 1 z z
ij 2
t s t i 1, j t i 1, j
(11)
z z z
150 ° W
°
30 W 4
t i , j 1 t i , j 1 t ij
° ° the Jacobi operator:
120 W 60 W
°
90 W
1
J ij , z i 1, j i 1, j z i , j 1 z i , j 1
4s 2
Fig. 2. Stereographic projection of the northern hemisphere and the 16×19
rectangular grid structure for CFvN calculations. (12)
i, j 1
i , j 1 z i 1, j z i 1, j
where
is the geographical latitude. z
The boundary conditions for are:
r is the distance from the pole on the stereographic t
projection map. The radius of the equator on the map
was chosen as the unit of distance. z z z z
0 (13)
m is the magnification factor of the polar stereographic t 0 j t pj t i 0 t iq
projection.
f is the Coriolis parameter. i 0, ..., p; j 0, ..., q
is the angular velocity of Earth’s rotation
which means the geopotential height is considered to be
(=2π(24·60·60)-1 rad/s).
constant at the boundaries during the term of prediction.
g is the gravitational constant (g=9.80665 m/s2).
However, the boundary values of are different in cases
The finite difference vorticity equations of CFvN that have t ij
been implemented in our system are the following: when the fluid is entering or leaving the investigated area. In
ij hij ij f ij (7) the first case 0 and in the second case can be
ij
t t ij
calculated by linear extrapolation from the interior value of
ij
J ij , z (8) and z:
t
z ij 0 : 2
ij (9)
0 j
t 1 j t 2 j
t
t t i 0 : z 0, j 1 z 0, j 1 (14)
0 : 0
t 0 j
where
ij z ij (10)
This equation is used for the calculation of ij in the
first step of the iteration while in the following steps
(24) is used.
ISSN 1844 – 9689 http://cjece.ubm.roA. Vas et al. / Carpathian Journal of Electronic and Computer Engineering 6/1 (2013) 56-63 59
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3) ( 7 )
z ij (
10 )
ij ( ij (
12 )
0 : 2
pj
t p 1, j t p 2, j
t n times iteration
i p : z p, j 1 z p , j 1 of (8),( 9 ),(11) (19)
z
0 : 0 J ij , z
for the whole field
t pj t ij
(15) At the first step on the border nodes ij are extrapolated
similarly to (14)-(17):
0 : 2
i 0 : 0 j 21 j 2 j (20)
j 0 : z i -1,0
z i 1, 0
t
i0
i1 t i 2
t (16)
0 :
0 i p : pj 2 p 1, j p 2, j (21)
t i 0
j 0 : i 0 2 i1 i 2 (22)
0 : 2
t iq t i , q 1 t i , q 2
j q : z i 1, q z i 1, q j q : iq 2 i ,q 1 i ,q 2 (23)
0 : 0
t iq
During this procedure the nodes are communicating with
their neighbors, exchanging data and solving the differential
(17) equation by applying finite difference scheme (19). Since the
iterative solution of the finite difference scheme can be
i 0, ..., p; j 0, ..., q explained as the propagation of disturbances in the field of the
investigated area, the data change and the finite difference
The corner points are not taken into consideration. iteration parts of the calculation for the different nodes in our
case can happen not only in a regular way, but even randomly.
In a worldwide network of DSN-PC the boundary
condition may not necessarily be defined in the above way z
When and are determined from (11) and
since the nodes of the network will provide them t ij t ij
automatically through their directly measured and calculated
data. (12), the time extrapolation can be done using the next
equations [4]:
z
The explicit solution for shown in [4] that was
t ij
ij t 0 t ij t 0 t t 0
more suitable for the ENIAC calculation procedure, and is t ij
given by four one-dimensional Fourier transforms:
ij t t ij t t 2t t (24)
t ij
z s 2 p 1 q 1 p 1 q 1
t ij pq z
zij t0 t zij t 0 t t 0
l 1 m 1 r 1 s 1
2 l m
1
t ij
sin sin 2 (18)
2p 2q t rs z
zij t t zij t t 2t t (25)
lr ms li mj t ij
sin sin sin sin
p q p q
These calculations have to be repeated 24 times for the
However, in our system this method would require from whole forecast period and the solution can be found iteratively
each DSN-PC node to collect data from all the other nodes of z
the investigated area, which would be difficult and would by solving for and extrapolating the motion forward in
t ij
require large memory and processor capacities. Therefore, in
our system an iterative solution, calculated in a distributed time with the suitable boundary conditions. The flowchart of
way by the µC based nodes, was applied, that consists of the the algorithm is shown in Fig. 3. Initial steps including the
next steps: calculation of the geographical parameters are omitted for
better readability.
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Calculate predicted
geopotential height (z) Calculate η (7)
Node
inner position ? border
Node
inner position ? border
Wait until inner nodes
Get z and η from neighbors
Wait until inner nodes finish calculation of ∂ξ/∂t
Get z from neighbors
finish calculation of ξ
Calculate ∂ξ/∂t (12)
Get z from 2 border neighbors
Get ξ from 2 inner neighbors
Calculate ξ (10)
counter=0
Check conditionA. Vas et al. / Carpathian Journal of Electronic and Computer Engineering 6/1 (2013) 56-63 61
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Fig. 5. The test environment with 3 real weather stations connected to each
Fig. 4. Our prototype DSN-PC station [9]. other and to the simulated environment through an Ethernet switch. For better
understanding, the 16×19 rectangular grid (Fig. 2) is represented on grid
paper.
B. Software on the DSN-PC panel
For embedded software development we used MPLAB X, IV. RESULTS
an integrated development environment from Microchip and
The initial observed data of the 500 mbar geopotential
the TCP/IP Stack library, which includes the source code of
height is represented on the map of Fig. 6, and the map of the
many network communication protocols.
24 hour later observed data is shown in Fig. 7. The necessary
Based on that library, the most important parts of our data in both cases are the same as they were in the original
software are the UDP servers and clients responsible for the CFvN calculations and are taken from [11]. The original
communication between the stations over the network. UDP is solution on the ENIAC [4] as well as P. Lynch’s
currently preferred to TCP because the PIC18F67J60 μCs only demonstrations on MATLAB and mobile phone [11],[12],[13]
have 4 kB of data memory, and UDP requires significantly all apply (18). However, in our DSN-PC system, the
less memory. application of the iterative method (19) is more suitable, since
for one node it is sufficient to know the necessary data of their
Previously three calculation methods have been close and distant neighbors, and do not need to collect and
implemented such as temperature gradients, isotherms and the store the whole data set from all the other nodes of the
solution of heat transfer equation by FDM [9]. Since we do investigated area. The result of the 24 hour geopotential height
not have our own forecast algorithm for DSN-PC yet, but we CFvN prediction calculation by our DSN-PC system, which
wanted to show its capability making not only simple applies (19) can be seen in Fig. 8.
calculations and solving the simple heat transfer equation but
solving more difficult differential equations related to weather It agrees well with the previous results (Fig. 9)
prediction calculations; the well-known first successful [4],[11],[12],[13], and the difference between those and ours
method of CFvN was implemented. are negligible (Fig. 10), which shows that our method and a
DSN-PC-like system may have to be applied for making more
As soon as the final system is available, an efficient way of sophisticated weather prediction calculations in the future.
firmware (FW) updates is going to be essential, especially in
the early phase of the development. The FW update V. CONCLUSION
mechanism needs a boot loader, which is able to download a
new version of FW if available and apply the update. It is On the base of our conception we succeeded to design and
important to guarantee that a corrupted communication cannot develop instruments and architecture, as well as to build the
prevent the boot loader from getting back to normal operation. prototype of a meteorological Network for Sensing and
Microchip’s Library for Applications contains a demo numerical weather Prediction Calculations (DSN-PC). As it
application called Internet Bootloader which fits our was shown earlier, the present system is capable of sensing
requirements. Based on that demo a customized version was temperature, pressure and humidity besides calculating
made, which is integrated with a symmetric encryption isotherms, temperature gradients and solving simple numerical
method based on XTEA cipher for increased security. The differential equations like heat transfer by the method of finite
boot loader application is based on a TFTP server, listening differences [9]. The system is working through the Internet,
for incoming connection on UDP port 69. In the case of an where the nodes receive the measured parameters from their
incoming connection the server waits for incoming data from close and distant neighbors and make the necessary
the client and downloads the new FW. For easier usability we calculations. Here the conception and structure of DSN-PC
are working on a TFTP client based version, so it will be able was described, furthermore the implementation of the well-
to automatically check for a new version on an update server, known finite-difference vorticity equations of CFvN on our
download the new FW and reprogram the µC. system is shown to demonstrate its capability of making
simple weather prediction calculations in a test environment.
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5000 5000 5600 5405200 560
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56
5000
520540
00
5600 0 0 0
4800 480
00
5600
0 00
560 5400 00
52
0
500 50 0 0
52 50 5000 00
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580 0 0 580 5800 5800 5800 5800
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5800
5800 5800
Fig. 7. The final observed 500 mbar geopotential height weather map
(24 hours later) [4],[11],[12].
Fig.6. The initial observed 500 mbar geopotential height weather map as the
input of CFvN calculations [4],[11],[12]. developing new stations with extended sensor
capabilities, increased measurement accuracy and
Although the present system consists of only 3 stations and improved networking functions such as applying GPS
the other nodes of the applied virtual field are simulated, it receiver and long range radiowave or GSM connection.
was possible to investigate several different hardware
configurations, the applied algorithms and software as well as at the present a central computer is needed to help the
to get sufficient experiences for further developments of our nodes to find their neighbors when a new node is
DSN-PC system. Some of the further possibilities are: introduced to the system, that could be eliminated by
applying a neighbor discovery algorithm running on
developing modern suitable weather prediction the stations.
algorithms (i.e. method of finite elements with irregular
net) for DSN-PC. using the system not only for weather sensing and
prediction but also for other FDM/FEM systems.
applying it in short-term regional weather forecast or
urban climate and heat island analysis. applying forecast calculation methods on mobile
phones equipped with i.e. air pressure sensors.
increasing the order of calculations.
involving vertical data in the calculations. 560 540 5000 56
5200
0 0 4800 00
5000 5600
5600
5200
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5400
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4800
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Fig. 8. The result of 24 hour 500 mbar geopotential height CFvN weather Fig. 9. The result of 24 hour 500 mbar geopotential height CFvN weather
prediction calculation by using the iterative solution (19) and our prototype prediction calculation by using (18) and P. Lynch’s open source MATLAB
DSN-PC system in the test environment. code [11],[12].
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0 0.20 0 0 −0.20 0
ACKNOWLEDGMENT
0.4 0.2 −0.4 0.2
−0. 0 −0− The authors wish to thank SciTech Műszer Kft. for
0
2 0 .2 − .4 providing the possibility to use their facilities and for
0 − 0.6
0.4
0.2 supporting our work financially.
4 6
0.4 −0. −0. .8
0
0.6 REFERENCES
−0
0
−0.2
−0.2
0
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can be applied in different research and university programs,
we make the
circuit diagram of our present DSN-PC station
the embedded software of measurements, Ethernet
communication, existing calculations etc.
the Java software of DSN-PC simulation environment
freely available on http://www.scitechmuszer.com for non-
commercial developments and university programs;
furthermore, we are open for future cooperation.
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