Dept of Bioenvironmental Systems Engineering National Taiwan University Lab for Remote Sensing Hydrology and Spatial Modeling Raingauge Network Evaluation and Augmentation Using Geostatistics Ke-Sheng Cheng Department of Bioenvironmental Systems Engineering National Taiwan University

Introduction Rainfall data is essential in many hydrological applications including water budget analysis, frequency analysis and stormwater drainage design. Direct measurement of rainfall can only be achieved by raingauges and raingauge networks are often installed to provide measurements that characterize the temporal and spatial variations of rainfall.

The level of accuracy a network can achieve depends on the total number and locations of gauges in the network. The required minimum density of a raingauge network is dependent on the time resolution (or scale) of the desired rainfall measurements and their spatial variability.

Many approaches of optimal selection of the rainfall gauges take into account the number and location of rainfall gauges which yield greater accuracy of areal rainfall estimation with minimum cost. These approaches are generally known as the variance reduction method which involves searching for the appropriate number of rainfall gauges and their locations.

For such applications, performance evaluation of a network focuses on reducing the estimation variance of the area average rainfall. Variances of individual point rainfall estimations, especially at ungauged locations, are not considered.

In many applications, using areal rainfall as input to hydrological models may be enough for flood forecasting since catchments behave as low-pass filters and the necessary intervals for rainfall measurements in time and in space may be determined by variability in the discharge at the watershed outlet.

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However, most tributaries of river systems in Taiwan have steep slops and respond quickly to local rainfalls which often are very intense. As a result, monitoring localized high intensity rainfalls becomes immensely important and raingauge networks have been installed tailoring to such needs.

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The purpose of this study is to propose a raingauge network evaluation and augmentation approach focusing on accuracy assessment of point rainfall estimation across the whole study area.

Study area and data The Danshuei River Basin downstream from the Shihmen Reservoir in northern Taiwan was selected for this study. Area: 2200 km 2 Hourly rainfall data from 1990 to 2004 recorded at 27 raingauge sites were collected. Average annual rainfall: 2,800 mm. Terrain elevation: 0 – 1000 m above the mean sea level.

Study area and raingauges

Considerations on scale and spatial variability Scale Water resources management and planning long duration rainfall (daily, 10-day period, monthly, annual) Flood forecasting and stormwater management short duration rainfall (hourly, or even shorter) Design of a raingauge network should base on its functional objective, which in turn also determines the duration of rainfall for analysis. Spatial variability time scale and storm-type dependent Orographic effect Proportional effect

Season-specific dominant storm types Winter frontal rainfall (from November to early April of the next year) Mei-Yu ( from late April to mid- to end of June) Convective rainfall and typhoons (both from July to October)

Variogram analysis The random nature of spatial variation of many natural phenomena can be described by a random field Z(x) where x represents the spatial location and Z is the random phenomenon under investigation. The spatial variation structure of a random field Z(x) can be represented by its variogram defined as:

Variogram analysis Storm events of various seasons and intensities have different spatial variation structures; therefore, it is not realistic to adopt a unique variogram for all storm events, irrespective of rainfall intensities, and seasonal and meteorological conditions.

Orographic effect If a spatial trend or orographic effect of the expected value of Z(x) exists, the random field Z(x) is not stationary and the variogram may increase without a sill. Therefore, it is necessary to check for orographic effect or trend existence of E[Z(x)] prior to variogram modeling.

Proportional effect Random fields with higher measurement values tend to have higher degree of variability. This is known as the proportional effect in geostatistics.

Climatological or dimensionless variogram model

Orographic effect of the average annual rainfall

Proportional effect of Mei-Yu hourly rainfall

The experimental and fitted dimensionless variograms of hourly Mei-Yu rainfall

Raingauge network evaluation and augmentation For the purpose of water resources planning, a low density network may be enough to capture the spatial variability of longer duration rainfalls; while a high density raingauge network is required for flood forecasting and mitigation. Among the four major storm types, hourly rainfalls of Mei-Yu have the highest spatial variability and therefore are considered as the basis for subsequent network evaluation and design.

In evaluating and designing a raingauge network the major concern is how to quantify the performance of an existing or proposed network. The proposed network may be a chosen subset of the existing network, augmentation of a subset (including the whole set) of the existing network, or a new network including the augmented network and newly added gauges.

Measuring network performance Intuitively, a measure of the network performance is the accuracy associated with estimates of the areal average or point rainfalls. The accuracy should reflect not only the absolute error but also the error variance since the errors depend heavily on rain field variability, and this variability is far from being consistent from one event to another and one year to the next.

If only unbiased estimators are considered, the characteristics of estimation accuracy can thus be focused on the variance of estimation error. Using the error variance as a measure of network performance implies that the evaluation is conducted on an ensemble basis.

The estimation accuracy of point rainfall varies within the study area and is dependent on the number and geometric layout of raingauges. In practice, a good raingauge network should yield acceptable accuracy for most points within the study area.

Defining the acceptable accuracy

Ordinary kriging estimation

It s worthy to note that, given the variogram (h), the ordinary kriging variance can be calculated without measurements of Z(x i ). The kriging variance depends entirely on the geometric configuration of x i and x 0.

Probability distribution of the estimation error under different kriging variances Estimated from the dimensionless variogram of z

Points associated with higher kriging variances correspond to lower acceptance probabilities, and all points with acceptance probability lower than are considered not having acceptable accuracy. It is worthy to note that for our study is determined as the sill value of the dimensionless variogram since rainfall data were preprocessed.

The experimental and fitted dimensionless variograms of hourly Mei-Yu rainfall Sill =

Network performance evaluation based on the percentage of area with acceptable accuracy Performance evaluation of a raingauge network can be made based on the percentage of area with acceptable accuracy (hereafter expressed by A p ). Also, since the acceptance probability can be calculated at each point within the study area, contour map of acceptance probability can be developed to assist in evaluation and augmentation of an existing network.

The whole study area was discretized into a set of grid nodes with 1 km interval and acceptance probability at each node was calculated.

Contour maps of acceptance probability for hourly rainfall of Mei-Yu and annual rainfall

Hourly Mei-Yu Contour maps of acceptance probability

Annual rainfall Contour maps of acceptance probability

Evaluation of the existing network In comparison, for a fixed value of, say 0.8 or 0.9, annual rainfall is associated with a higher value of A p, due to its higher spatial correlation. For example, at = 0.8, about 56% of the total area has acceptable accuracy for hourly rainfall, whereas 82% of the total area has acceptable accuracy for annual rainfall.

It can also be observed that A p values are very low at = 0.9 (16% and 36% for hourly Mei-Yu and annual rainfalls respectively), suggesting that = 0.9 may not be a realistic choice for the study area. If a threshold value of A p, say 60%, is set as the network evaluation and augmentation criterion, then at = 0.8, the current network can barely meet the criterion. However, if the threshold is set at a higher level, say 80%, then the current network fails the evaluation and network augmentation is necessitated.

Augmentation of an existing raingauge network An existing network can be augmented in terms of the percentage of area with acceptable accuracy by relocating the existing gauges or adding new gauges. A sequential algorithm is devised to prioritize the existing raingauges and to sequentially evaluate the joint performance of a subset of raingauges.

Upon completion of the sequential algorithm, all raingauges are prioritized according to their order of removal from the network. In addition, at each stage when a gauge is removed, contour maps of acceptance probability and their corresponding A p values were also established using only the remaining gauges. These information form the basis of the proposed raingauge network augmentation approach.

Using the values of A p corresponding to removal of individual raingauges, or equivalently a set of remaining gauges, illustrative figures can be constructed to show the prioritized order of raingauges and performance of a subset of raingauges.

Raingauge prioritization and corresponding A p values. (a) Hourly rainfall of Mei-Yu. (b) Annual rainfall. Note: (1) = 0.8, (2) the number adjacent to a point represents the gauge number.

Hourly rainfall of Mei-Yu

Study area and raingauges

Annual rainfall

It can be seen clearly that for hourly Mei- Yu rainfall, at = 0.8, with only 19 gauges (gauges 4, 22, 2, 10, 11, 16, 18, and 15 were sequentially removed) the remaining network can achieve almost the same level of A p as the complete network of 27 gauges. These remaining gauges form the base network and will not be relocated in the subsequent network augmentation process.

Contour map of the acceptance probability established by the base network of hourly Mei-Yu rainfall Hourly Mei-Yu Base network Contour maps of acceptance probability

Hourly Mei-Yu All gauges Contour maps of acceptance probability

Similarly, for annual rainfall, the base network is comprised of only 15 gauges (gauges 2, 4, 5, 11, 12, 22, 9, 10, 25, 13, 16 and 14 were sequentially removed) and still can achieve almost the same level of A p as the complete network.

Raingauges not being included in the base network are redundant and provide little contribution to the network. These raingauges can either be abolished to reduce the maintenance cost or relocated to achieve higher level of A p.

Relocating raingauges can again be conducted in a sequential manner. The first relocated point is determined by searching one point among all points with which, together with the base network, yields the highest value of A p.

Such search generally does not take much efforts since, with the base network in place, most points already have. The rest relocated points can then be sequentially determined in a similar manner.

Contour map of acceptance probability of hourly rainfall established by the augmented network which includes the base network and all relocated gauges.

For the hourly Mei-Yu rainfall case, A p increases quickly and reaches 88% when all non-base gauges are relocated. The amount of increase in A p (about 32%) is very significant and demonstrates the applicability of the proposed network augmentation approach. However, it may not always be necessary to relocate all non-base gauges. For the annual rainfall case, the value of A p reaches almost 100% after only three or four non-base gauges are relocated, and therefore relocating more gauges is unnecessary.

If the threshold value of 80% is set for A p of hourly Mei-Yu, after relocation of five non-base gauges the augmented network yields a higher-than-80% A p, and relocation of the other three non-base gauges is not necessary.

Summary A geostatistical approach for raingauge network evaluation and augmentation was proposed. The approach takes into account the spatial variation of uncertainties in rainfall spatial estimation. Accuracy assessment is based on a criterion for variance of estimation error. Network augmentation can be conducted based on the proportion of area with acceptable accuracy.

Thank you for your attention. Your comments are most welcome.

Rainfall of different storm types exhibit different degrees of spatial variation. For example, hourly rainfall of convective storms and typhoons exhibits higher spatial variation whereas the hourly frontal rainfall is less variable in space. In addition, long-duration (for example, monthly, seasonal and annual) rainfalls tend to be more spatially homogeneous than hourly and daily rainfalls.

Sequential algorithm

Mei-Yu rainfalls are produced by surface frontal systems which advance southeastward from southern China to Taiwan from mid- to late spring through early to midsummer each year. The fronts are usually accompanied by a synoptic-scale cloud band with embedded mesoscale convective systems (MCSs), extending several thousand kilometers from southern Japan to southern China with an approximately east – west orientation (Yeh, et al., 2002). During the passage of a Mei-Yu frontal system, a few very active mesoscale convective cells may develop repeatedly, causing heavy and localized rainfall for the area. Although the synoptic-scale frontal system may last for a few days, the MCSs generally have lifetime of a few hours to one day only.