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Indian Journal of Radio & Space Physics Vol. 31, June 2002, pp. 155-158

Comparison of evaporation duct models to compute duct height over Arabian sea and Bay of Bengal

P K Pasricha, M V S N Prasad & S K Sarkar

Radio and Atmospheric Sciences Division, National Physical Laboratory, New Delhi 110 012

Received 18 December 2001; revised I2 February 2002; accepted 15 March 2002

Various models exist that calculate evaporation duct height in terms of directly measureable meteorological parameters in the surface layer over the sea-surface. One of these models (Paulus-Jeske model) is a straightforward model employing certain empirical formulae, and the other (Babin-Young-Carton model) an exhaustive model employing Monin-Obukhov similarity theory. In this paper, a comparison is made between these two models for 'a test data set' off the coast of California and sample marine data over the Arabian sea and Bay of Bengal. The applications of these two models to compute evaporation duct heights over the warm tropical oceans are highlighted.

1 Introduction Anomalous propagation of electromagnetic

radiation in the surface layer over the ocean may cause radio/radar signals to propagate in such a manner that the curvature of their path is greater than the curvature of the earth's surface. The radiowaves may then get trapped within this ducting layer, and travel beyond the horizon. The most prevalent type of anomalous propagation over the ocean is due to a phenomenon called evaporation ducting. Evaporation ducts are formed due to the rapid decrease in water vapour content which, in tum, leads to a rapid decrease in the radio refractivity within about twenty metres over the sea-surface. Propagation of microwaves in the atmosphere is determined by gradients of the radio refractivity (N) of air. The radio refractivity gradient (dN/dz) is, in tum, given in terms of the gradients of atmospheric pressure, water vapour pressure and temperature. The height of the evaporation duct is defined as the height at which dN/dz is -0.157 N-units per metre. Evaporation ducts are almost always present over the sea-surface, yet their heights are highly variable in space and time. There are two basic evaporation duct models that are in use to compute the duct height. These are Paulus­Jeske modell.2 and Babin-Young-Carton model3

. The effects of evaporation ducts on radar and communications performance have been discussed by a number of workers4-- 16. The problems caused by evaporation ducts are manifold: (i) a radar loses contact with low flying targets, (ii) line-of-sight communication is extended to much larger ranges beyond the horizon, (iii) a complete loss of signal

occurs in the so-called shadow zone, (iv) radar's scope is full of noise (or atmospheric clutter) even when sea is calm (or with no sea clutter), etc. Microwave propagation models, such as 'Tropospheric Electromagnetic Parabolic Equation Routine (TEMPER), and the 'Integrated Refractive Effects Prediction System (IREPS), are used to predict radar and communication performance for a

. f d' . 17 18 gIven set 0 con ItIOns . .

The limited scope of the present paper is to make a comparison between the duct height calculated with the straightforward Paulus-Jeske model with the comprehensive Babin-Young-Carton model for (i) the Babin's test data off the coast of California and (ii) sample marine data over the Arabian sea and over the Bay of Bengal over different seasons.

2 Models of evaporation duct height There are basically two models for computing

evaporation duct height, namely, Paulus-Jeske model l

.2 and Babin-Young-Carton modee. In these

models the computation of evaporation duct height involves finding of an expression for the vertical refractivity gradient in terms of directly measured meteorological parameters I9

-21 . The similarity theory

of Monin-Obukhov is used to describe turbulence and stability conditions in the surface layer over the sea­surface. Recently, indirect attempts have been made to derive radio refractivity over the sea-surface through remote sensing by using an emitter and a number of receiver arrays22 and from radar sea­clutter23

.

156 INDIAN J RADIO & SPACE PHYS, JUNE 2002

2.1 Paulus-Jeske model The Paulus-Jeske (PI) model has been perhaps the

most widely used evaporation duct height model. The model uses air temperature and relative humidity at 10 m and sea-surface temperature as inputs. The model uses empirically the bulk Richardson number and Obukhov length in order to categorize atmospheric stability conditions. The evaporation duct height is the height at which radio refractivity gradient for ducting has a critical value of -0.157 N­units per metre. The PJ model equation for computing duct height (Zd in metres) may be approximately given as3

:

Zd = - O.06[C (es -ea)+B (Ts -Ta)]

A +0.157 .. . (1)

where, the constant') A, Band C are related to the refractivity gradient through the equation

dN = A dp + B dT + C de dz dz dz dz

. . . (2)

where, N is the radio refractivity, p the atmospheric pressure (mbar), Ta the deck-level atmospheric temperature (OC), Ts the sea-surface temperature (0C), ea the deck level vapour pressure (mbar) and es the sea-surface vapour pressure (mbar). The constants A, B and C are the same in Eqs (1) and (2), and are known in terms of absolute values of ea, Ta and p. Here, N = (n-l) 106

, where n is the atmospheric refractive index. The values of constants A, Band C are experimentally determined as -0.030, -1.30 and 4.5, respectively.

2.2 Babin-Young-Carton model The PI model depends on empirically derived

relationships between Richardson number and Obukhov length for various computations. In the Babin-Young-Carton (BYC) model these empirical relationships are replaced with those obtained from surface-layer physics, such as those of Fairall et al. 24

•25

• The BYC model has been shown to estimate the evaporation duct height within 1 m. The BYC model equations to evaluate duct height (Zd in metres) under unstable and stable conditions are given by3:

.~.

Zd = - (BT * +Cq*) «P

0.4 (A + 0.157) . .. (3)

and

- (BT *+Cq*) Zd = 5 .. . (4)

0.4 (A + 0.157) + - (BT * +Cq*) . L

where, the parameters T* (DC), q* (kglkg) and «P (the profile function) are the Monin-Obukhov parameters, which are evaluated through the similarity theori, and the constants A, Band C are evaluated through the following equations:

A = (-o.OI)dag [77.6 + 481Ox77.6 q ] _ T T 2 {E + (l - E) q}

- g {p-O-E)e} _ [-7~.6 - 23

X48 10X77.6 q] cpa T T {E + (l - E) q}

(5)

B=(~) RIc [-77.6 - 2x481Ox77.6 qp] l1000 T2 T3 {E - (1- E) q}

... (6)

C = 4810x 77.6 T 2 {E - (1- E ) q}

... (7)

where, q is the specific humidity (kg/kg), p the atmospheric pressure (mbar), e the vapour pressure (mbar), da the air density (kg/m3

), T the air temperature CC), g the acceleration due to gravity, Ra the dry-air gas constant, cpa the dry-air specific heat and E = 0.62197.

The evaporation duct height is obtained by iteratively solving Eq. (3) for unstable conditions and Eq. (4) for stable conditions.

3 Meteorological measurements o'Ver the sea­surface for computing evaporation duct height The maritime observations on the sea-surface

temperature, and deck level observations on pressure, temperature, dew point (and hence specific humidity) and wind speed were obtained from the Marine Climatological Summaries prepared by the India Meteorological Department (lMD) under the auspices of the WMO. These observations are of routine type, and are made by ships of Voluntary Observing Fleet. The data are available from 1966 onwards at IMD, Pune, on payment basis. Monthly mean observations

\ )-

PASRICHA el al.: COMPARISON OF EV APORATION DUCT MODELS 157

pertammg to winter, summer and eqinoxes over the Arabian sea and Bay of Bengal were adopted for the present study.

4 Evaluation of duct height in Paulus-Jeske (PJ) model, and constants (A, Band C) and duct height in Babin-Young-Carton (BYC) model A computer software to evaluate duct heights in the

Pl and BYC models has been developed. Whereas evaluation of duct height in the Pl model is straightforward, the evaluation of duct height in the BYC model consists of the following three steps:

(i) Evaluate constants A, Band C in terms of e, T and p through Eqs (4), (5) and (6).

(ii) Evaluate parameters L, T* and q*. (iii) Solve Eq. (3) for Zd, iteratively, within 0.1 m of

the old duct height value.

5 Results Some salient features of the results on comparison

between the constants (A, Band C) and the duct height for the two evaporation duct models are as follows.

5.1 Evaluation of constants A, Band C and duct height in BYC model using Babin's test data

Babin's test data consists of the following data, namely, measurement height = 6 m, sea-surface

Table I-Comparison of constants A, Band C. and duct height in Paulus-leske (Pl) and Babin-Young-Carton (BYC) models using

Babin's test data

Source

Pl model

BYC model

Constants A B

-0.030 -1.30

-0.027 -1.24

C

4.50

4.93

Duct height

m

4.5

4.5

temperature = 2.2°C, temperature at 6 m = 1.6°C, relative humidity at 6 m = 73.3%, wind speed at 6 m = 4.6 m S-l and atmospheric pressure = 1024.15 mbar. A comparison of constants A, Band C in Sec. 2.1 and those obtained through BYC model in Sec. 2.2, using Babin's test data is given in Table l. It is seen that the two sets of constants are not much different from each other for the 'cold water' sea off California's coast to which the data pertains. Table 1 also gives duct height evaluated through both the Pl and the BYC models. Again, the duct height calculated through the two models are almost the same for the Babin's test data.

5.2 Evaluation of duct height using pj and BYC models over Arabian sea and Bay of Bengal during winter and summer

Both these models were originally developed based on meteorological inputs from cold temperate oceans. It is instructive to see how these models fare when applied to warm tropical oceans . Formation of evaporation ducts and their characteristics over tropical oceans markedly differ from that over temperate oceans. Sample duct height calculations have been made using the Pl and BYC models over the Arabian sea and Bay of Bengal during the winter and summer periods. Their comparison is given in Table 2. It is seen that the values obtained in the BYC model are lower than those in the Pl model. The monthly variability in duct height during both the winter and summer months over the Arabian sea and Bay of Bengal is ± 1 m and ± 2 m, respectively.

5.3 Evaluation of duct height using pj and BYC models over Arabian sea and Bay of Bengal during eqinoxes

Sample duct height calculations have been made using the Pl and BYC models over the Arabian sea and Bay of Bengal during the eqi noxes. Their comparison is given in Table 3. It is again seen that the values obtained from the BYC model are lower

Table 2-Comparison of duct heights using Paulus-leske (Pl) and Babin-Young-Carton (BYC) models over Arabian sea and Bay of Bengal during winter and summer

Constants Duct height (m) Arabian sea Bay of Bengal Arabian sea Bay of Bengal

Winter Summer Winter Summer Winter Summer Winter Summer

pj model A=-0.030 -0.030 -0.030 -0.030 16.3±1 20.8±1 13.6±2 26.0±2 B=-1 .30. -1.30 -1.30 -1 .30 C=4.50 4.50 4.50 4.50

BYCmodel A=-0.026 -0.02 -0.025 -0.027 10.5±1 12.2±1 11.8±2 13.8±2 8=-1.55 -1.63 -1.49 -1.73 C=4.17 4.02 4.13 3.95

158 INDIAN J RADIO & SPACE PHYS, JUNE 2002

Table 3--Comparison of duct heights using Paulus - Jeske (PJ) and Babin- Young -Carton (BYC) models over Arabian sea and

Bay of Bengal during equinoxes

Constants Duct height (m) Arabian sea Bay of Bengal Arabian sea Bay of Bengal

PJ model A=-0.030 -0.030 24.3 24.1 8=-1.30 -1.30 C=4.50 4.50

Bye model A=-0.026 -0.026 9.5 10.7 8=-1.67 -1.70 C=4.01 4.01

than those from the PJ model. The monthly variability in duct height over both the Arabian sea and Bay of Bengal is ± 2 m.

6 Summary and conclusion Evaporation ducts are the most common cause of

anomalous propagation over the ocean surface. These ducts tend to trap micro- and millimetre waves, and thereby affect radar-sea-surface detectability, ship-to­ship communications, ship-to-shore communications and ship-to-satellite communications at low grazing angles. The height of these ducts is the critical input parameter for varIous propagation models. A comparison is made between the duct height calculated with the latest Babin-Young-Carton (B YC) model with the straightforward Paulus-Jeske (Pl) model using the test data of Babin et al. 3 and sample data over the Arabian sea and Bay of Bengal. Babin's test data off the coast of California reveals that the calculated duct height is the same for the two models. The duct height calculated with the BYC model over the Indian ocean is always lower than that calculated with the PJ model. The advantage of PJ model is its computational simplicity which is generally preferred by system engineers. Real-time meteorological measurements over the sea-surface to compute evaporation duct heights are planned in the future. It will enable one to develop/modify the existing models so that they are suitable for tropica l co nditions.

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