Author: Marta Balagu´e Mart´ınez
Facultat de F´ısica, Universitat de Barcelona, Diagonal 645, 08028 Barcelona, Spain.
Advisor: Joan Bech Rustullet
Abstract: In this study, disdrometer observations are used to obtain and analyze the Z-R re- lationships for the region divided by the Urgell channel near Lleida (NE Spain). The differences induced by surface characteristics in the relationships are not obvious since, for both irrigated and non-irrigated areas, the exponents and prefactors of the resulting relations are almost identical.
Rainfall rate in the non-irrigated is generally greater than in the irrigated area, specially in summer.
A seasonal analysis shows the highest prefactors in summer, the highest exponents in winter and the lowest prefactors and exponents in spring. Rainfall rate estimates perform well for both the fitted relationship obtained and the Marshall-Palmer relation for continental stratiform precipitation.
I. INTRODUCTION
The measurement and prediction of the temporal and spatial distribution of rainfall is the primary concern of hydrometeorology. Weather radars usually only offer the aloft reflectivity factor Z, which is then converted into the rainfall rate R, at ground level. The estimation of rainfall may be impacted by how this conversion is carried out;
this is known as the observer’s problem [1]. The standard procedure for over 70 years has been to take a power law relationship between Z and R (3). Since both factors rely on the raindrop size distribution (DSD), which is regu- lated by the microphysical processes in a precipitating system, it is also known that aspects like location, sea- son, synoptic situation and rainfall types influence the coefficients of the relationships [2].
The issue faced by the observer’s problem can be par- tially resolved, for example, by using an optical disdrom- eter. Installed at ground level and based on optical atten- uation, this device detects the size and velocity of falling particles crossing a laser beam. Because it allows for the acquisition of the DSD, it is possible to obtain both Z and R independently, thus the power law coefficients by fitting a linear model [3].
In the framework of the ‘Land surface Interaction with the Atmosphere over the Iberian Semi-arid Environment’
(LIAISE) project [4], this study is aimed to examine po- tential differences in hydrometeorological variables in a region where the land characteristics display an abrupt change in terrain features, with one area being irrigated and the other non-irrigated, which are separated by the Urgell channel. This work will analyze radar reflectivity and rainfall rate from four disdrometers, which are evenly distributed between the irrigated and non-irrigated areas.
The time frame covers from April 2021 to June 2022, which includes the campaign period (May to September 2021).
The main goal is to compute the Z-R relationships and compare them to the literature. Additionally, ex- amine the seasonal variability and use the relationships obtained to determine the errors induced in estimating rainfall rates.
II. METHODOLOGY
Four different disdrometers were used to acquire data:
two in the comarca of Urgell (T`arrega and Tordera) for which the terrain presents irrigation and two in Pla d’Urgell (Mollerussa and La Cendrosa) for which the area is rainfed (details shown in TABLE I). The disdrometers used are OTT Parsivel2 [5] and they issue records every 60 seconds with information about the size and fall ve- locities of precipitation particles. These parameters are stored in a two-dimensional matrix that subdivides each particle into 32 x 32 classes. The radar reflectivity fac- tor Z (mm6 m−3) and the rainfall rate R (mm h−1) are obtained via the following equations [6], for which Z is expressed in decibel units, being 1 dBZ = 10 log10(Z):
dBZ = 10 log10X
i
N (D)iD6i∆Di (1)
and
R = 3.6 · 10−3π 6
X
i
N (D)iD3iV (D)i∆Di (2)
where D (mm) is the diameter, N(D) (m−3 mm−1) is the DSD and V(D) (m s−1) is the terminal velocity pro- posed by [7]. A linear model can be fitted using dBZ and log10(R), assuming the variables are related by the following power law:
Z = ARb (3)
dBZ = intercept + slope · log10(R) (4)
dBZ = 10 log10(A) + b · 10 log10(R) (5) Therefore, by comparing equations (4) and (5), the coefficients A and b are determined [3]:
A = 10intercept10 (6)
b = slope
10 (7)
TABLE I: Information about every disdrometer dataset used for this study. QC stands for quality control.
Name Location Area Operational
Period
Missing Data
Raw Data Points
(min)
Data Points after QC
(min) T`arrega 41.667◦N;1.162◦E Irrigated 04/05/2021 -
15/06/2022 24/11/2021 14383 5764
Tordera 41.681◦N;1.223◦E Irrigated 30/04/2021 -
15/06/2022 None 16461 7249
Mollerussa 41.618◦N;0.871◦E Non-Irrigated 27/04/2021- 19/06/2022
07/09/2021 -
13/09/2021 13763 5486
La Cendrosa 41.693◦N;0.928◦E Non-Irrigated 09/04/2021 - 13/10/2021
13/05/2021 -
01/07/2021 4706 1731
A quality control has been applied to ensure the ex- clusion of solid and mixed phase particles, as well as non meteorological signals or errors associated with border effects [8]. The filtering criteria are as follows:
- Drops whose fall speed differs by ±50% from the threshold set by V(D) are removed.
- Only 1 min data points with more than 100 detected particles and R > 0.05 mm h−1 during at least 3 consec- utive minutes are considered valid.
A total of 20230 1 min data points were quantified after applying the quality control.
III. RESULTS
A. Rainfall Rate Analysis
Firstly, the pattern of the rainfall rate of the total dataset will be examined. The seasonal distribution of R, dividing between irrigated and non-irrigated areas is shown in FIG. 1 in the format of violin plots (DJF for winter, MAM for spring, JJA for summer and SON for autumn). The violin for summer differs the most from the rest. For this season, the Q1 and Q3 have values of 1.0 mm h−1 and 4.9 mm h−1 for the irrigated area, and 1.4 mm h−1 and 5.9 mm h−1 for the non-irrigated.
The dispersion is relatively large in both areas with in- terquartile range values (Q3 - Q1) of 3.9 mm h−1 for the irrigated and 4.5 mm h−1 for the non-irrigated. The median value in summer on the irrigated area is 1.9 mm h−1, while for the non-irrigated is 2.7 mm h−1, being the latter higher. The maximum values are also in sum- mer, with 145.98 mm h−1 for the irrigated, and 146.77 mm h−1 for the non-irrigated. For winter, it is also no- ticeable that the Q3 is lower for the non-irrigated area, with a value of 1.2 mm h−1, whereas for the irrigated is 1.4 mm h−1. The minimum values registered occur in spring, with 0.06 mm h−1 for the irrigated, and 0.08 mm h−1 for the non-irrigated. The median values for the remaining seasons and for all data are similar, with the non-irrigated median being slightly higher in each case.
This distribution shows values typically associated with stratiform (R < 10 mm h−1) rainfall type (96.8%
of all data), and only 3.2% present values with R ≥ 10 mm h−1, usually associated with convective rainfall [9].
According to previous research [10], the accumulated pre- cipitation for the campaign period on the non-irrigated area presents greater values in spring and summer than in the irrigated one, showing the existence of a zonal gra- dient increasing semi-arid conditions (drier and warmer) from east to west. However, this does not imply that a direct relationship could be set between higher accumu- lated precipitation and greater rainfall rates.
FIG. 1: Seasonal distribution of the rainfall rate R dividing by terrain features. The horizontal axis labels represent each season (DJF for winter, MAM for spring, JJA for summer and SON for autumn). To make it easier to directly compare the distributions, half a violin is represented for each area and the densities are cut on the maximum and minimum values.
The upper and lower lines represent the quartiles Q1 and Q3 (25 and 75 percentile) while the mid-line shows the median value. A violin for the total dataset over the whole operational period is also included.
B. Z-R Scatterplots
For all data gathered by the four disdrometers, the scatterplot of Z-R is shown in FIG. 2. A linear model fit has been applied to the data following equations (6,7);
with resulting power law coefficients A = 184 and b =
FIG. 2: Z-R scatterplot for the entire dataset. The Z = ARb linear fit is represented as a solid black line. The values of the coefficients and exponents for the fitted power law are shown.
The Marshall-Palmer relation for continental stratiform rain [11] is presented in a solid magenta line.
1.68, and a correlation coefficient of r2 = 0.96. The rainfall rate values vary from 0.06 to 146.77 mm h−1, while the reflectivity values range from 0.03 to 62.80 dBZ.
There is a noticeable dense concentration of values be- tween 10 and 40 dBZ, corresponding mostly to moder- ate, stratiform rain conditions [9]. For rain rates below 0.2 mm h−1and above 20.0 mm h−1, the number of data points decreases, and the dispersion becomes larger.
The Marshall-Palmer (ZM −P) relation for continental stratiform rain can also be found in FIG. 2. This re- lationship was chosen for comparison because it is the most widely used and it has a close correspondence for rain rates between 1 and 50 mm h−1 [11]. For the range of densely concentrated values, both expressions overlay.
At high rain rates, ZM −P would overestimate rainfall,
whereas for low rain rates, it would underestimate it. For a given Z, the fitted Z-R relationship provides R values that are comparable to those associated with stratiform rainfall type, since this type of rain makes up almost the total precipitation contribution for the entire dataset.
When examining the datasets separating by irrigated and non-irrigated areas, the Z-R relationships are nearly identical in both cases (Zir = 188R1.67 and Znir = 182R1.68), with their associated linear regressions ap- pearing to be aligned (not shown). For the total number of data points, it initially seems as though there is no evidence of a connection between Z-R and the land fea- tures. However, there may be differences when dividing by seasons.
FIG. 3 shows the scatterplots of the total dataset di- vided by meteorological seasons. In FIG. 3a), which cor- responds to all data, it can be noticed that winter (5.86%
of all data) has the lowest density; possibly partially con- ditioned by the disdrometer of La Cendrosa, which did not record any data in that season. Spring has the high- est density (58.71%), followed by autumn (25.35%) and summer (10.08%). In winter, the data points present low reflectivity and low rain rate values, with a small region going from 0.1 to 1.0 mm h−1, displaying higher R values for the same Z. In summer, the data points are mostly located in the region with high R and Z values (≥ 10 mm h−1 and ≥ 40 dBZ), where the dispersion increases and the values are typically associated with convective rain. It can also be noticed that summer has a steeper slope, while for winter is less steep. The measured vari- ables for spring and autumn take similar values for the whole range, with spring showing the lowest value in the dataset.
In FIG. 3b) and 3c), the Z-R scatterplots for the irri- gated and non-irrigated areas, respectively, can be found.
Both plots have roughly the same large, disperse form, with a density of values similar to the total dataset case.
For the irrigated area: 55.11% belongs to spring, 8.50%
to summer, 30.79% to autumn and 5.60% to winter.
FIG. 3: Z-R scatterplots differentiating by seasons: a) total dataset; b) irrigated area; c) non-irrigated area. The fitted linear regressions are presented in solid lines. The values of the coefficients and exponents are also shown.
FIG. 4: Scatterplot of the power laws coefficient A and exponent b for: a) total dataset; b) irrigated area; c) non-irrigated area.
Each symbol corresponds to a certain season and the black ones represent the sum for the entire study period.
For the non-irrigated area: 60.70% belongs to spring, 10.95% to summer, 22.34% to autumn and 6.01% to win- ter. One difference is that, for the data points in the region with high R values corresponding to autumn, the linear regression is aligned with the spring one for the irrigated area, while in the non-irrigated, the autumn re- gression is overlapped with the summer one. Another difference is that the small region of winter values men- tioned before, visibly belongs to the non-irrigated case.
Additionally, for the non-irrigated area, there are more summer data points with lower R values.
C. Z-R Relationships
1. Power Law Coefficients
The prefactor A and exponent b can differ from one site to the next, as well as between seasons. They ex- hibit the characteristics of a given location’s or season’s climatology, or more precisely, the kind of rainfall from which they are derived [1]. The obtained coefficients for this study’s dataset will be examined in this section.
FIG. 4 displays the scatterplot of A and b of the fit- ted power laws for all data, irrigated and non-irrigated areas, also diving each category by seasons. We can ob- serve that A has values between 173 and 230, and b has values between 1.59 and 1.86. Most of the obtained ex- ponents also have values that are somewhat greater than or similar to the M-P exponent of 1.60.
There is a clear pattern between the three graphs, with the Z-R relationships being almost identical in summer, spring and for the total dataset. Summer displays the highest prefactor in all three cases. Spring, on the other hand, displays the lowest prefactor and exponent values.
Although it can be challenging to clearly link the coeffi- cients to specific types of rainfall, it is possible to identify some broad trends. The summer tendency could indi- cate a convective footprint (lower exponent and higher prefactor) [2], related with the fact that radar reflectiv-
ity is more sensitive to raindrop diameters [1] and sum- mer typically presents larger drops (not shown). Winter, on the contrary, shows stratiform rainfall characteristics (smaller prefactors and larger exponents). As for the distinction between irrigated and non-irrigated, it is no- ticeable that there is no apparent differences when aver- aging, since the black symbols (all stations in each area and for the total study period) are in the same posi- tion. However, autumn in the non-irrigated area shows a close resemblance with summer, whereas in the irrigated it aligns more with spring. Winter in the non-irrigated also shows the highest exponent value.
2. Estimation of rainfall rates
TABLE II lists the errors associated with estimating rainfall rates obtained from reflectivity alone using the reverse R(Z) relationships. Rexprepresents experimental results, Remp empirical results from fitting the relations obtained in section III.B, and RM −P derived from the Marshall-Palmer expression. All acquired estimated val- ues have the same order of magnitude as the experimental ones. The mean values are similar, with a discrepancy of 0.17 mm h−1 and 0.31 mm h−1, respectively. The stan- dard deviations are larger in both cases, with the M-P being 2.69 mm h−1 greater than the experimental one.
SEM values are also nearly identical, whereas the RMSE value for the M-P relationship is 1.04 mm h−1 higher.
Even if the results show a promising fit between the experimental and estimated values, the following state- ments must be considered [9]:
1. When estimating radar rainfall rates using dis- drometer data, radar errors and measurement dwell times are not taken into account.
2. The results must be repeatable to have operational significance.
3. For different microphysical precipitation systems,
one would need to employ multiple Z-R relation- ships, so an additional classification step of precip- itation types would be necessary.
TABLE II: Summary of the mean, standard deviation, stan- dard error of the mean (SEM) and root mean square error (RMSE) values for the experimental and estimated rainfall rates. Rexpare the study’s total dataset values, Rempderived from Z = 184R1.68and RM −P from ZM −P = 200R1.60.
Mean Standard
Dev. SEM RMSE
Rexp (mm h−1) 2.62 6.41 0.045 - Remp(mm h−1) 2.79 7.68 0.054 3.53 RM −P (mm h−1) 2.93 9.10 0.064 4.57
IV. CONCLUSIONS
All of the objectives set for this research have been successfully accomplished. The use of disdrometer data allowed the radar reflectivity and rainfall rate variables to be calculated independently.
The following conclusions were drawn after analyzing the results:
- The distinction between irrigated and non-irrigated areas considered in this study has a minor influence on the Z-R relationships.
- The rainfall rate median values are similar in both areas, with the non-irrigated median being always slightly higher, specially in summer, for which the rates also present the highest values.
- A seasonal breakdown shows the highest prefactors in summer, the highest exponents in winter and the lowest prefactors and exponents in spring.
- The relationships obtained successfully estimate rainfall rate values and the Marshall-Palmer rela- tion fits the data quite accurately, possibly imply- ing an overall stratiform footprint. However, this should not be considered as final since no rainfall type differentiation has been applied.
To avoid biased results in future projects aimed at fit- ting Z-R relations, a proper distinction between rainfall types could be performed, considering they have an influ- ence on the DSD. A comparison with rain gauges and a closer examination of the precipitation episodes, as well as the quality control, should also be done, since the amount of minutes removed is more than half and could result in underestimations.
On a more personal level, this work has improved my programming skills, as well as introduced me to the use of disdrometers, an instrument I was previously unfamiliar with.
Acknowledgments
I would like start by expressing my gratitude to Joan Bech, my advisor, for all of his insightful remarks and guidance on my research work. Likewise, I want to thank Queralt Calder´on and all the members of the Grup de Meteorologia UB, as well as, Enric Casellas and Sergi Gonz`alez, for their considerate assistance even when it was not required. Finally, I want to express my gratitude to my family, especially my loving mother, and to my dear friends (Jordi, Arnau, Vane, David, Laura, Marc, Romeu, Cram and Chris) for their unconditional support.
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